Dmitriy Bilyk

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All published works

Action	Title	Year	Authors
+ PDF Chat	Regularizing random points by deleting a few	2025	Dmitriy Bilyk Stefan Steinerberger
+ PDF Chat	Positive definite singular kernels on two-point homogeneous spaces	2024	Dmitriy Bilyk Peter J. Grabner
+ PDF Chat	Geodesic Distance Riesz Energy on Projective Spaces	2024	Dmitriy Bilyk Ryan Matzke Joel Nathe
+ PDF Chat	Optimizers of three-point energies and nearly orthogonal sets	2024	Dmitriy Bilyk Damir Ferizović Alexey Glazyrin Ryan Matzke Josiah Park Oleksandr Vlasiuk
+ PDF Chat	Single radius spherical cap discrepancy via gegenbadly approximable numbers	2024	Dmitriy Bilyk Michelle Mastrianni Stefan Steinerberger
+	Experimental Survey of Discrete Minimizers of the $p-\text{frame}$ Energy	2023	Dmitriy Bilyk Alexey Glazyrin Ryan Matzke Josiah Park Oleksandr Vlasiuk
+ PDF Chat	Lower Bounds for the Directional Discrepancy with Respect to an Interval of Rotations	2023	Dmitriy Bilyk Michelle Mastrianni
+	Polarization and Greedy Energy on the Sphere	2023	Dmitriy Bilyk Michelle Mastrianni Ryan Matzke Stefan Steinerberger
+	Optimizers of three-point energies and nearly orthogonal sets	2023	Dmitriy Bilyk Damir Ferizović Alexey Glazyrin Ryan Matzke Josiah Park Oleksandr Vlasiuk
+	Optimal Measures for Multivariate Geometric Potentials	2023	Dmitriy Bilyk Damir Ferizović Alexey Glazyrin Ryan Matzke Josiah Park Oleksandr Vlasiuk
+	A random line intersects $\mathbb{S}^2$ in two probabilistically independent locations	2023	Dmitriy Bilyk Alan Chang Otte Heinävaara Ryan Matzke Stefan Steinerberger
+	Single radius spherical cap discrepancy via gegenbadly approximable numbers	2023	Dmitriy Bilyk Michelle Mastrianni Stefan Steinerberger
+ PDF Chat	Positive definiteness and the Stolarsky invariance principle	2022	Dmitriy Bilyk Ryan Matzke Oleksandr Vlasiuk
+ PDF Chat	Potential theory with multivariate kernels	2022	Dmitriy Bilyk Damir Ferizović Alexey Glazyrin Ryan W. Matzke Josiah Park Oleksandr Vlasiuk
+ PDF Chat	Optimal measures for $p$-frame energies on spheres	2022	Dmitriy Bilyk Alexey Glazyrin Ryan Matzke Josiah Park Oleksandr Vlasiuk
+	Lower bounds for the directional discrepancy with respect to an interval of rotations	2022	Dmitriy Bilyk Michelle Mastrianni
+ PDF Chat	Energy on spheres and discreteness of minimizing measures	2021	Dmitriy Bilyk Alexey Glazyrin Ryan Matzke Josiah Park Oleksandr Vlasiuk
+	Potential theory with multivariate kernels	2021	Dmitriy Bilyk Damir Ferizović Alexey Glazyrin Ryan Matzke Josiah Park Oleksandr Vlasiuk
+	Positive definiteness and the Stolarsky invariance principle	2021	Dmitriy Bilyk Ryan Matzke Oleksandr Vlasiuk
+	1. On some recent developments in uniform distribution and discrepancy theory	2020	Dmitriy Bilyk
+	Energy on spheres and discreteness of minimizing measures	2019	Dmitriy Bilyk Alexey Glazyrin Ryan Matzke Josiah Park Oleksandr Vlasiuk
+	Optimal measures for p-frame energies on spheres	2019	Dmitriy Bilyk Alexey Glazyrin Ryan Matzke Josiah Park Oleksandr Vlasiuk
+	Energy on spheres and discreteness of minimizing measures	2019	Dmitriy Bilyk Alexey Glazyrin Ryan Matzke Josiah Park Oleksandr Vlasiuk
+	Optimal measures for p-frame energies on spheres	2019	Dmitriy Bilyk Alexey Glazyrin Ryan Matzke Josiah Park Oleksandr Vlasiuk
+	Geodesic distance Riesz energy on the sphere	2018	Dmitriy Bilyk Chang‐Feng Dai
+ PDF Chat	General and refined Montgomery Lemmata	2018	Dmitriy Bilyk Chang‐Feng Dai Stefan Steinerberger
+	On the Fejes Tóth problem about the sum of angles between lines	2018	Dmitriy Bilyk Ryan Matzke
+ PDF Chat	BMO and exponential Orlicz space estimates of the discrepancy function in arbitrary dimension	2018	Dmitriy Bilyk Lev Markhasin
+	On the Fejes T\'oth Problem about the Sum of Angles Between Lines	2018	Dmitriy Bilyk Ryan Matzke
+	General and Refined Montgomery Lemmata	2018	Dmitriy Bilyk Chang‐Feng Dai Stefan Steinerberger
+ PDF Chat	The Stolarsky Principle and Energy Optimization on the Sphere	2018	Dmitriy Bilyk Feng Dai Ryan Matzke
+ PDF Chat	Tusnády’s Problem, the Transference Principle, and Non-uniform QMC Sampling	2018	Christoph Aistleitner Dmitriy Bilyk Aleksandar Nikolov
+	On the Fejes Tóth Problem about the Sum of Angles Between Lines	2018	Dmitriy Bilyk Ryan Matzke
+	General and Refined Montgomery Lemmata	2018	Dmitriy Bilyk Dai Feng Stefan Steinerberger
+	One-bit sensing, discrepancy and Stolarsky's principle	2017	Dmitriy Bilyk Michael T. Lacey
+	Tusn\'ady's problem, the transference principle, and non-uniform QMC sampling	2017	Christoph Aistleitner Dmitriy Bilyk Aleksandar Nikolov
+	One-bit sensing, discrepancy and Stolarsky's principle	2017	Dmitriy Bilyk Michael T. Lacey
+	Tusnády's problem, the transference principle, and non-uniform QMC sampling	2017	Christoph Aistleitner Dmitriy Bilyk Aleksandar Nikolov
+	Stolarsky principle and energy optimization on the sphere	2016	Dmitriy Bilyk Feng Dai Ryan Matzke
+ PDF Chat	The Two-Dimensional Small Ball Inequality and Binary Nets	2016	Dmitriy Bilyk Naomi Feldheim
+	Geodesic distance Riesz energy on the sphere	2016	Dmitriy Bilyk Chang‐Feng Dai
+	Stolarsky principle and energy optimization on the sphere	2016	Dmitriy Bilyk Dai Feng Ryan Matzke
+	The two-dimensional small ball inequality and binary nets	2015	Dmitriy Bilyk Naomi Feldheim
+	Diophantine approximations and directional discrepancy of rotated lattices	2015	Dmitriy Bilyk Xiaomin Ma Jill Pipher Craig Spencer
+	One Bit Sensing, Discrepancy, and Stolarsky Principle	2015	Dmitriy Bilyk Michael T. Lacey
+	Random Tessellations, Restricted Isometric Embeddings, and One Bit Sensing	2015	Dmitriy Bilyk Michael T. Lacey
+	The two-dimensional small ball inequality and binary nets	2015	Dmitriy Bilyk Naomi Feldheim
+	BMO and exponential Orlicz space estimates of the discrepancy function in arbitrary dimension	2014	Dmitriy Bilyk Lev Markhasin
+ PDF Chat	BMO and exponential Orlicz space estimates of the discrepancy function in arbitrary dimension	2014	Dmitriy Bilyk Lev Markhasin
+	Discrepancy theory and harmonic analysis	2014	Dmitriy Bilyk
+	Roth’s Orthogonal Function Method in Discrepancy Theory and Some New Connections	2014	Dmitriy Bilyk
+	Discrepancy theory and harmonic analysis.	2014	Dmitriy Bilyk
+	BMO and exponential Orlicz space estimates of the discrepancy function in arbitrary dimension	2014	Dmitriy Bilyk Lev Markhasin
+	Dichotomy results for the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math>norm of the discrepancy function	2013	Gagik Amirkhanyan Dmitriy Bilyk Michael T. Lacey
+	Estimates of the Discrepancy Function in Exponential Orlicz Spaces	2013	Gagik Amirkhanyan Dmitriy Bilyk Michael T. Lacey
+ PDF Chat	The Supremum Norm of the Discrepancy Function: Recent Results and Connections	2013	Dmitriy Bilyk Michael T. Lacey
+	The L 2 Discrepancy of Irrational Lattices	2013	Dmitriy Bilyk
+	Estimates of the Discrepancy Function in Exponential Orlicz Spaces	2013	Gagik Amirkhanyan Dmitriy Bilyk Michael T. Lacey
+	The L 2 Discrepancy of Two-Dimensional Lattices	2012	Dmitriy Bilyk Vladimir Temlyakov Rui Yu
+	On the Scientific Work of Konstantin Ilyich Oskolkov	2012	Dmitriy Bilyk Laura De Carli Alexander Petukhov Alexander M. Stokolos Brett D. Wick
+ PDF Chat	Directional discrepancy in two dimensions	2011	Dmitriy Bilyk Xiaomin Ma Jill Pipher Craig Spencer
+	Fibonacci sets and symmetrization in discrepancy theory	2011	Dmitriy Bilyk Vladimir Temlyakov Rui Yu
+ PDF Chat	Exponential Squared Integrability of the Discrepancy Function in Two Dimensions	2009	Dmitriy Bilyk Michael T. Lacey Ioannis Parissis Armen Vagharshakyan
+ PDF Chat	Cyclic shifts of the van der Corput set	2009	Dmitriy Bilyk
+ PDF Chat	Composition of Haar paraproducts: the random case	2009	Dmitriy Bilyk Michael T. Lacey Xiaochun Li Brett D. Wick
+	A Three Dimensional Signed Small Ball Inequality	2009	Dmitriy Bilyk Michael T. Lacey Ioannis Parissis Armen Vagharshakyan
+	On the signed small ball inequality	2008	Dmitriy Bilyk Michael T. Lacey Armen Vagharshakyan
+ PDF Chat	On the small ball inequality in three dimensions	2008	Dmitriy Bilyk Michael T. Lacey
+	Cyclic shifts of the van der Corput set	2008	Dmitriy Bilyk
+	On the Small Ball Inequality in all dimensions	2007	Dmitriy Bilyk Michael T. Lacey Armen Vagharshakyan
+	On the Signed Small Ball Inequality	2007	Dmitriy Bilyk Michael T. Lacey Armen Vagharshakyan
+	Distributional estimates for the bilinear Hilbert transform	2006	Dmitriy Bilyk Loukas Grafakos
+	INTERPLAY BETWEEN DISTRIBUTIONAL ESTIMATES AND BOUNDEDNESS IN HARMONIC ANALYSIS	2005	Dmitriy Bilyk Loukas Grafakos

Common Coauthors

Coauthor	Papers Together
Ryan Matzke	22
Michael T. Lacey	15
Oleksandr Vlasiuk	14
Josiah Park	12
Alexey Glazyrin	12
Stefan Steinerberger	8
Armen Vagharshakyan	5
Damir Ferizović	5
Lev Markhasin	4
Michelle Mastrianni	4
Chang‐Feng Dai	4
Aleksandar Nikolov	3
Gagik Amirkhanyan	3
Christoph Aistleitner	3
Naomi Feldheim	3
Brett D. Wick	2
Jill Pipher	2
Craig Spencer	2
Rui Yu	2
Ioannis Parissis	2
Loukas Grafakos	2
Vladimir Temlyakov	2
Dai Feng	2
Xiaomin Ma	2
Feng Dai	2
Peter J. Grabner	1
Joel Nathe	1
Michelle Mastrianni	1
Xiaochun Li	1
Alexander M. Stokolos	1
Ryan W. Matzke	1
Alan Chang	1
Otte Heinävaara	1
Laura De Carli	1
Alexander Petukhov	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	On irregularities of distribution	1954	K. F. Roth	22
+	Irregularities of Distribution	1987	József Beck William Chen	15
+	On the Small Ball Inequality in all dimensions	2007	Dmitriy Bilyk Michael T. Lacey Armen Vagharshakyan	14
+ PDF Chat	Irregularities of distribution, VII	1972	Wolfgang Schmidt	14
+ PDF Chat	Sums of Distances Between Points on a Sphere	1972	Kenneth B. Stolarsky	13
+	None	2003	John J. Benedetto Matthew Fickus	13
+ PDF Chat	On the small ball inequality in three dimensions	2008	Dmitriy Bilyk Michael T. Lacey	11
+ PDF Chat	Some upper bounds in the theory of irregularities of distribution	1984	József Beck	10
+	Explicit constructions in the classical mean squares problem in irregularities of point distribution	2002	William Chen M. M. Skriganov	10
+ PDF Chat	The Small Ball Problem for the Brownian Sheet	1994	Michel Talagrand	10
+	Uniform distribution of sequences	1974	L. Kuipers Harald Niederreiter	9
+	Note on irregularities of distribution	1956	H. Davenport	9
+	Sums of distances between points on a sphere — an application of the theory of irregularities of distribution to discrete Geometry	1984	József Beck	9
+ PDF Chat	On irregularities of distribution, III	1979	K. Roth	9
+ PDF Chat	Minimization of the probabilistic p-frame potential	2011	Martin Ehler Kasso A. Okoudjou	9
+	A simple proof of Stolarsky’s invariance principle	2013	Johann S. Brauchart Josef Dick	9
+	Digital Nets and Sequences	2010	Josef Dick Friedrich Pillichshammer	9
+	On irregularities of distribution	1980	William Chen	9
+	Harmonic analysis on totally disconnected groups and irregularities of point distributions	2006	M. M. Skriganov	8
+ PDF Chat	Exponential Squared Integrability of the Discrepancy Function in Two Dimensions	2009	Dmitriy Bilyk Michael T. Lacey Ioannis Parissis Armen Vagharshakyan	8
+	Über eine Punktverteilung auf der Kugel	1959	László Tóth	7
+ PDF Chat	Sums of distances between points on a sphere. II	1973	Kenneth B. Stolarsky	7
+	An Inequality for Trigonometric Polynomials and Its Application for Estimating the Entropy Numbers	1995	Vladimir Temlyakov	7
+ PDF Chat	The Stolarsky Principle and Energy Optimization on the Sphere	2018	Dmitriy Bilyk Feng Dai Ryan Matzke	7
+	Positive definite functions on spheres	1942	I. J. Schoenberg	7
+	Geometric Discrepancy	1999	Jiřı́ Matoušek	7
+ PDF Chat	Irregularities of distribution. I	1987	József Beck	7
+	Multiparameter operators and sharp weighted inequalities	1997	Robert Fefferman Jill Pipher	7
+	Geometry of minimizers for the interaction energy with mildly repulsive potentials	2016	José A. Carrillo Alessio Figalli Francesco S. Patacchini	6
+ PDF Chat	Symmetric informationally complete positive-operator-valued measures: A new computer study	2010	A.J. Scott Markus Grassl	6
+	Geodesic distance Riesz energy on the sphere	2018	Dmitriy Bilyk Chang‐Feng Dai	6
+	A two-dimensional van Aardenne-Ehrenfest theorem in irregularities of distribution	1989	József Beck	6
+	The extreme and L2 discrepancies of some plane sets	1969	John H. Halton S. K. Zaremba	6
+	Some weighted norm inequalities concerning the schrödinger operators	1985	Sun Chang Jeremy M. Wilson Thomas Wolff	6
+ PDF Chat	On the Support of Minimizers of Causal Variational Principles	2013	Felix Finster Daniela Schiefeneder	6
+	Number Theory and Algebra	1995	Rajeev Motwani Prabhakar Raghavan	6
+ PDF Chat	On the discrepancy function in arbitrary dimension, close to L 1	2008	Michael T. Lacey	5
+	On the Signed Small Ball Inequality	2007	Dmitriy Bilyk Michael T. Lacey Armen Vagharshakyan	5
+	ON IRREGULARITIES OF DISTRIBUTION II	1983	William Chen	5
+	Cubature formulas, discrepancy, and nonlinear approximation	2003	Vladimir Temlyakov	5
+	Orthogonality and Digit Shifts in the Classical Mean Squares Problem in Irregularities of Point Distribution	2008	William Chen M. M. Skriganov	5
+	Universally optimal distribution of points on spheres	2006	Henry Cohn Abhinav Kumar	5
+ PDF Chat	Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates	2003	José A. Carrillo Robert J. McCann Cédric Villani	5
+ PDF Chat	Sharp square-function inequalities for conditionally symmetric martingales	1991	Gang Wang	5
+ PDF Chat	Nonlocal Interaction Equations in Environments with Heterogeneities and Boundaries	2015	Lijiang Wu Dejan Slepčev	5
+	Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis	1994	Hugh L. Montgomery	5
+ PDF Chat	Symmetric informationally complete quantum measurements	2004	Joseph M. Renes Robin Blume-Kohout A.J. Scott Carlton M. Caves	5
+	Spherical codes and designs	1977	P. Delsarte J.-M. Goethals J.J. Seidel	5
+	Mutual interactions, potentials, and individual distance in a social aggregation	2003	Alex Mogilner L. Bent Äthan Spiros Leah Edelstein‐Keshet	5
+ PDF Chat	Nonlocal interactions by repulsive–attractive potentials: Radial ins/stability	2012	D. Balagué José A. Carrillo Thomas Laurent Gaël Raoul	5