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The largest slice of fractal percolation
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2025
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Pablo Shmerkin
Ville Suomala
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On the Distance Sets Spanned by Sets of Dimension d/2 in $\mathbb{R}^{d}$
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2025
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Pablo Shmerkin
Hong Wang
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Dimensions of Furstenberg sets and an extension of Bourgainâs projection theorem
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2024
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Pablo Shmerkin
Hong Wang
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PDF
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Covering the SierpiĆski carpet with tubes
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2024
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Aleksi PyörÀlÀ
Pablo Shmerkin
Ville Suomala
Meng Wu
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Dynamical self-similarity, $L^{q}$-dimensions and Furstenberg slicing in
$\mathbb{R}^d$
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2024
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Emilio Corso
Pablo Shmerkin
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On the dimension of orthogonal projections of self-similar measures
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2024
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Amir Algom
Pablo Shmerkin
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Kaufman and Falconer Estimates for Radial Projections and a Continuum Version of Beckâs Theorem
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2024
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Tuomas Orponen
Pablo Shmerkin
Hong Wang
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Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory
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2023
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Tuomas Orponen
Pablo Shmerkin
Hong Wang
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Slices and distances: on two problems of Furstenberg and Falconer
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2023
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Pablo Shmerkin
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On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane
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2023
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Tuomas Orponen
Pablo Shmerkin
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Inverse theorems for discretized sums and $L^q$ norms of convolutions in $\mathbb{R}^d$
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2023
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Pablo Shmerkin
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On the Fourier decay of multiplicative convolutions
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2023
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Tuomas Orponen
Nicolas de Saxcé
Pablo Shmerkin
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On the volumes of simplices determined by a subset of $\mathbb{R}^d$
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2023
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Pablo Shmerkin
Alexia Yavicoli
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A non-linear version of Bourgainâs projection theorem
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2022
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Pablo Shmerkin
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On the packing dimension of Furstenberg sets
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2022
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Pablo Shmerkin
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PDF
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New bounds on Cantor maximal operators
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2022
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Pablo Shmerkin
Ville Suomala
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On normal numbers and self-similar measures
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2022
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Amir Algom
Simon Baker
Pablo Shmerkin
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On exceptional sets of radial projections
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2022
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Tuomas Orponen
Pablo Shmerkin
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Kaufman and Falconer estimates for radial projections and a continuum version of Beck's Theorem
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2022
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Tuomas Orponen
Pablo Shmerkin
Sheng Wang
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Dimensions of Furstenberg sets and an extension of Bourgain's projection theorem
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2022
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Pablo Shmerkin
Sheng Wang
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+
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On normal numbers and self-similar measures
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2021
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Amir Algom
Simon Baker
Pablo Shmerkin
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PDF
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On sets containing a unit distance in every direction
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2021
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Pablo Shmerkin
Han Yu
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An improved bound for the dimension of $(\alpha,2\alpha)$-Furstenberg sets
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2021
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Kornélia Héra
Pablo Shmerkin
Alexia Yavicoli
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PDF
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Assouad dimension influences the box and packing dimensions of orthogonal projections
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2021
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K. J. Falconer
Jonathan M. Fraser
Pablo Shmerkin
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PDF
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Improved Bounds on the Dimensions of Sets that Avoid Approximate Arithmetic Progressions
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2021
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Jonathan M. Fraser
Pablo Shmerkin
Alexia Yavicoli
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On the distance sets spanned by sets of dimension $d/2$ in $\mathbb{R}^d$
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2021
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Pablo Shmerkin
Hong Wang
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On normal numbers and self-similar measures
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2021
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Amir Algom
Simon Baker
Pablo Shmerkin
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+
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New bounds on Cantor maximal operators
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2021
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Pablo Shmerkin
Ville Suomala
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+
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On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane
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2021
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Tuomas Orponen
Pablo Shmerkin
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+
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Slices and distances: on two problems of Furstenberg and Falconer
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2021
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Pablo Shmerkin
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PDF
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Improved bounds for the dimensions of planar distance sets
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2020
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Pablo Shmerkin
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PDF
Chat
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On measures that improve $L^q$ dimension under convolution
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2020
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Eino Rossi
Pablo Shmerkin
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An improved bound for the dimension of $(\alpha,2\alpha)$-Furstenberg sets
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2020
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Kornélia Héra
Pablo Shmerkin
Alexia Yavicoli
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Maximal operators for cube skeletons
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2020
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Andrea Olivo
Pablo Shmerkin
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PDF
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Patterns in random fractals
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2020
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Pablo Shmerkin
Ville Suomala
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Covering the SierpiĆski carpet with tubes
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2020
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Aleksi PyörÀlÀ
Pablo Shmerkin
Ville Suomala
Meng Wu
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On the packing dimension of Furstenberg sets
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2020
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Pablo Shmerkin
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An improved bound for the dimension of $(α,2α)$-Furstenberg sets
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2020
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Kornélia Héra
Pablo Shmerkin
Alexia Yavicoli
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A nonlinear version of Bourgain's projection theorem
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2020
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Pablo Shmerkin
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+
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On sets containing a unit distance in every direction
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2019
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Pablo Shmerkin
Han Yu
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+
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Assouad dimension influences the box and packing dimensions of orthogonal projections
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2019
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K. J. Falconer
Jonathan M. Fraser
Pablo Shmerkin
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+
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Improved bounds on the dimensions of sets that avoid approximate arithmetic progressions
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2019
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Jonathan M. Fraser
Pablo Shmerkin
Alexia Yavicoli
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PDF
Chat
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New Bounds on the Dimensions of Planar Distance Sets
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2019
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TamĂ s Keleti
Pablo Shmerkin
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PDF
Chat
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Hölder coverings of sets of small dimension
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2019
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Eino Rossi
Pablo Shmerkin
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PDF
Chat
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On the Hausdorff dimension of pinned distance sets
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2019
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Pablo Shmerkin
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PDF
Chat
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On Furstenberg's intersection conjecture, self-similar measures, and the $L^q$ norms of convolutions
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2019
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Pablo Shmerkin
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PDF
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$$L^q$$ Dimensions of Self-similar Measures and Applications: A Survey
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2019
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Pablo Shmerkin
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$L^q$ dimensions of self-similar measures, and applications: a survey
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2019
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Pablo Shmerkin
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On sets containing a unit distance in every direction
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2019
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Pablo Shmerkin
Yu Han
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+
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Assouad dimension influences the box and packing dimensions of orthogonal projections
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2019
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K. J. Falconer
Jonathan M. Fraser
Pablo Shmerkin
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+
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Improved bounds on the dimensions of sets that avoid approximate arithmetic progressions
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2019
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Jonathan M. Fraser
Pablo Shmerkin
Alexia Yavicoli
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Arbeitsgemeinschaft: Additive Combinatorics, Entropy, and Fractal Geometry
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2018
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Emmanuel Breuillard
Michael Hochman
Pablo Shmerkin
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On measures that improve $L^q$ dimension under convolution
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2018
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Eino Rossi
Pablo Shmerkin
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Improved bounds for the dimensions of planar distance sets
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2018
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Pablo Shmerkin
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Self-similar measures: asymptotic bounds for the dimension and Fourier decay of smooth images
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2018
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Carolina A. Mosquera
Pablo Shmerkin
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Maximal Operators for cube skeletons
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2018
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Andrea Olivo
Pablo Shmerkin
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PDF
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Absolute continuity of non-homogeneous self-similar measures
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2018
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Santiago Saglietti
Pablo Shmerkin
Boris Solomyak
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PDF
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Squares and their centers
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2018
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TamĂ s Keleti
DĂĄniel T. Nagy
Pablo Shmerkin
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On measures that improve $L^q$ dimension under convolution
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2018
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Eino Rossi
Pablo Shmerkin
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+
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Improved bounds for the dimensions of planar distance sets
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2018
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Pablo Shmerkin
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+
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Maximal Operators for cube skeletons
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2018
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Andrea Olivo
Pablo Shmerkin
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+
PDF
Chat
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Spatially independent martingales, intersections, and applications
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2017
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Pablo Shmerkin
Ville Suomala
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Self-similar measures: asymptotic bounds for the dimension and Fourier decay of smooth images
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2017
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Carolina A. Mosquera
Pablo Shmerkin
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On equality of Hausdorff and affinity dimensions, via self-affine measures on positive subsystems
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2017
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Ian D. Morris
Pablo Shmerkin
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PDF
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On distance sets, box-counting and Ahlfors-regular sets
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2017
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Pablo Shmerkin
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Patterns in Random Fractals
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2017
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Pablo Shmerkin
Ville Suomala
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+
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H\"older coverings of sets of small dimension
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2017
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Eino Rossi
Pablo Shmerkin
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PDF
Chat
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A Class of Random Cantor Measures, with Applications
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2017
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Pablo Shmerkin
Ville Suomala
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Patterns in Random Fractals
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2017
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Pablo Shmerkin
Ville Suomala
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+
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Hölder coverings of sets of small dimension
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2017
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Eino Rossi
Pablo Shmerkin
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+
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Self-similar measures: asymptotic bounds for the dimension and Fourier decay of smooth images
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2017
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Carolina A. Mosquera
Pablo Shmerkin
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On Furstenberg's intersection conjecture, self-similar measures, and the $L^q$ norms of convolutions
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2016
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Pablo Shmerkin
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PDF
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<i>L</i><sup><i>q</i></sup>dimensions and projections of random measures
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2016
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Daniel Galicer
Santiago Saglietti
Pablo Shmerkin
Alexia Yavicoli
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PDF
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Salem Sets with No Arithmetic Progressions
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2016
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Pablo Shmerkin
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PDF
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Absolute continuity of complex Bernoulli convolutions
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2016
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Pablo Shmerkin
Boris Solomyak
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A class of random Cantor measures, with applications
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2016
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Pablo Shmerkin
Ville Suomala
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+
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On equality of Hausdorff and affinity dimensions, via self-affine measures on positive subsystems
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2016
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Ian D. Morris
Pablo Shmerkin
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A class of random Cantor measures, with applications
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2016
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Pablo Shmerkin
Ville Suomala
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+
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On Furstenberg's intersection conjecture, self-similar measures, and the $L^q$ norms of convolutions
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2016
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Pablo Shmerkin
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On equality of Hausdorff and affinity dimensions, via self-affine measures on positive subsystems
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2016
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Ian D. Morris
Pablo Shmerkin
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+
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Salem sets without arithmetic progressions
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2015
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Pablo Shmerkin
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PDF
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On the dimensions of a family of overlapping self-affine carpets
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2015
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Jonathan M. Fraser
Pablo Shmerkin
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PDF
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Dynamics of the scenery flow and geometry of measures
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2015
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Antti KÀenmÀki
Tuomas Sahlsten
Pablo Shmerkin
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PDF
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Absolute continuity of self-similar measures, their projections and convolutions
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2015
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Pablo Shmerkin
Boris Solomyak
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PDF
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Sets which are not tube null and intersection properties of random measures
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2015
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Pablo Shmerkin
Ville Suomala
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PDF
Chat
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Equidistribution from fractal measures
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2015
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Michael Hochman
Pablo Shmerkin
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PDF
Chat
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Structure of distributions generated by the scenery flow
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2015
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Antti KÀenmÀki
Tuomas Sahlsten
Pablo Shmerkin
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Projections of self-similar and related fractals: a survey of recent developments
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2015
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Pablo Shmerkin
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PDF
Chat
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Projections of Self-Similar and Related Fractals: A Survey of Recent Developments
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2015
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Pablo Shmerkin
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Spatially independent martingales, intersections, and applications
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2014
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Pablo Shmerkin
Ville Suomala
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+
PDF
Chat
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On the Exceptional Set for Absolute Continuity of Bernoulli Convolutions
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2014
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Pablo Shmerkin
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PDF
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Non-conformal Repellers and the Continuity of Pressure for Matrix Cocycles
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2014
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De-Jun Feng
Pablo Shmerkin
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On packing measures and a theorem of Besicovitch
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2014
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I. GarcıÌa
Pablo Shmerkin
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PDF
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Self-affine Sets and the Continuity of Subadditive Pressure
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2014
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Pablo Shmerkin
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Spatially independent martingales, intersections, and applications
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2014
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Pablo Shmerkin
Ville Suomala
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+
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On the exceptional set for absolute continuity of Bernoulli convolutions
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2013
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Pablo Shmerkin
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On the exceptional set for absolute continuity of Bernoulli convolutions
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2013
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Pablo Shmerkin
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Self-affine sets and the continuity of subadditive pressure
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2013
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Pablo Shmerkin
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Dimension, entropy and the local distribution of measures
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2012
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Tuomas Sahlsten
Pablo Shmerkin
Ville Suomala
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On packing measures and a theorem of Besicovitch
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2012
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I. GarcıÌa
Pablo Shmerkin
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PDF
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Visible parts of fractal percolation
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2012
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Ida Arhosalo
Esa JÀrvenpÀÀ
Maarit JÀrvenpÀÀ
MichaĆ Rams
Pablo Shmerkin
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PDF
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Local entropy averages and projections of fractal measures
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2012
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Michael Hochman
Pablo Shmerkin
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On packing measures and a theorem of Besicovitch
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2012
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Ignacio GarcĂaâFernĂĄndez
Pablo Shmerkin
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Porosity, dimension, and local entropies: a survey
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2011
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Pablo Shmerkin
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PDF
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Convolutions of cantor measures without resonance
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2011
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FĂ«dor Nazarov
Yuval Peres
Pablo Shmerkin
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PDF
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Multifractal structure of Bernoulli convolutions
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2011
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Thomas Jordan
Pablo Shmerkin
Boris Solomyak
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PDF
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The Dimension of Weakly Mean Porous Measures: a Probabilistic Approach
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2011
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Pablo Shmerkin
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Porosity, dimension, and local entropies: a survey
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2011
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Pablo Shmerkin
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Porosity, dimension, and local entropies: A survey.
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2011
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Pablo Shmerkin
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The dimension of weakly mean porous measures: a probabilistic approach
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2010
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Pablo Shmerkin
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PDF
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On the Dimension of Iterated Sumsets
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2010
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Jörg Schmeling
Pablo Shmerkin
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PDF
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The Hausdorff dimension of the projections of self-affine carpets
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2010
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Andrew Ferguson
Thomas Jordan
Pablo Shmerkin
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The dimension of weakly mean porous measures: a probabilistic approach
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2010
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Pablo Shmerkin
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On the dimension of iterated sumsets
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2009
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Jörg Schmeling
Pablo Shmerkin
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Convolutions of Cantor measures without resonance
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2009
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FĂ«dor Nazarov
Yuval Peres
Pablo Shmerkin
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The Hausdorff dimension of the projections of self-affine carpets
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2009
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Andrew Ferguson
Thomas Jordan
Pablo Shmerkin
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Visible parts of fractal percolation
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2009
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Ida Arhosalo
Esa JÀrvenpÀÀ
Maarit JÀrvenpÀÀ
MichaĆ Rams
Pablo Shmerkin
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On the dimension of iterated sumsets
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2009
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Jörg Schmeling
Pablo Shmerkin
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Convolutions of Cantor measures without resonance
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2009
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FĂ«dor Nazarov
Yuval Peres
Pablo Shmerkin
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+
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The Hausdorff dimension of the projections of self-affine carpets
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2009
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Andrew L. Ferguson
Thomas H. Jordan
Pablo Shmerkin
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PDF
Chat
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Overlapping self-affine sets of Kakeya type
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2008
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Antti KÀenmÀki
Pablo Shmerkin
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PDF
Chat
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Resonance between Cantor sets
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2008
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Yuval Peres
Pablo Shmerkin
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Moreira's Theorem on the arithmetic sum of dynamically defined Cantor sets
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2008
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Pablo Shmerkin
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Resonance between Cantor sets
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2007
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Yuval Peres
Pablo Shmerkin
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Resonance between Cantor sets
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2007
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Yuval Peres
Pablo Shmerkin
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PDF
Chat
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Zeros of {-1, 0, 1} Power Series and Connectedness Loci for Self-Affine Sets
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2006
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Pablo Shmerkin
Boris Solomyak
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PDF
Chat
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Overlapping self-affine sets
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2006
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Pablo Shmerkin
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PDF
Chat
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A Modified Multifractal Formalism for a Class of Self-similar Measures with Overlap
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2005
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Pablo Shmerkin
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Zeros of {-1,0,1}-power series and connectedness loci for self-affine sets
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2005
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Pablo Shmerkin
Boris Solomyak
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A Modified Multifractal Formalism for a Class of Self-Similar Measures
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2004
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Pablo Shmerkin
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A Modified Multifractal Formalism for a Class of Self-Similar Measures
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2004
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Pablo Shmerkin
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