Deterministic and probabilistic discrepancies

Type: Article

Publication Date: 2008-09-10

Citations: 16

DOI: https://doi.org/10.1007/s11512-008-0091-z

Abstract

In this paper, we compare some deterministic and probabilistic techniques in the study of upper bounds in problems related to certain mean square discrepancie with respect to balls in the d-dimensional unit torus, and show that the quality of these techniques depends in an intricate way on the dimension d under consideration.

Locations

  • Arkiv för matematik - View - PDF

Similar Works

Action Title Year Authors
+ PROBABILITY AND METRIC DISCREPANCY THEORY 2011 Christoph Aistleitner
István Berkes
+ Low-Discrepancy Sets for Axis-Parallel Boxes 1999 Jiřı́ Matoušek
+ PDF Chat Discrepancy for randomized Riemann sums 2009 Luca Brandolini
William Chen
Giacomo Gigante
Giancarlo Travaglini
+ Discrepancy and approximation of absolutely continuous measures with atomic measures 2023 Luca Brandolini
Leonardo Colzani
Giancarlo Travaglini
+ On a discrete approach to lower bounds in discrepancy theory 2023 Luca Brandolini
Bianca Gariboldi
Giacomo Gigante
Alessandro Monguzzi
+ Minimal dispersion on the cube and the torus 2024 A. Arman
Alexander E. Litvak
+ Some new lower bounds to centered and wrap-round -discrepancies 2012 Kashinath Chatterjee
Zhaohai Li
Hong Qin
+ Uniform Distribution Theory and Applications 2014 Michael Gnewuch
Frances Y. Kuo
Harald Niederreiter
Henryk Woźniakowski
+ Lower Bounds 1999 Jiřı́ Matoušek
+ The Discrepancy Method 1998 Bernard Chazelle
+ Discrepancy theory and related algorithms 2023 Nikhil Bansal
+ Upper Bounds in Classical Discrepancy Theory 2014 William Chen
M. M. Skriganov
+ Bounded discrepancy sets : (preprint) 1979 R. Tijdeman
Marc Voorhoeve
+ Deterministic error bounds 1988 Erich Novak
+ PDF Chat Minimal dispersion on the cube and the torus 2024 Andrii Arman
Alexander E. Litvak
+ Discrepancy Estimates on the Sphere 1999 В. В. Андриевскии
H.‐P. Blatt
M. Goütz
+ Original Article Error Bounds and Metric Subregularity 2014 Alexander Y. Kruger
+ Upper Bounds in Discrepancy Theory 2012 William Chen
+ Geometric discrepancy revisited 2002 Bernard Chazelle
+ Bounds for discrepancies in the Hamming space 2020 Alexander Barg
M. M. Skriganov