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On Bounds for the Concentration Function II

Authors
  • Deshouillers, Jean-Marc1
  • Freiman, Gregory A.2
  • Yudin, Alexander A.3
  • 1 Université Victor Segalen Bordeaux 2, Statistique Mathématique et Applications, Bordeaux, 33076, France , Bordeaux
  • 2 Tel Aviv University, Sackler Institute of Mathematics, Ramat Aviv, Israel , Ramat Aviv
  • 3 Vladimir Pedagogical University, Mathematic Department, Vladimir, 600 003, Russia , Vladimir
Type
Published Article
Journal
Journal of Theoretical Probability
Publisher
Kluwer Academic Publishers-Plenum Publishers
Publication Date
Jul 01, 2001
Volume
14
Issue
3
Pages
813–820
Identifiers
DOI: 10.1023/A:1017501308452
Source
Springer Nature
Keywords
License
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Abstract

We derive an upper bound for the concentration of the sum of i.i.d. random variables with values in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{Z}^d$$ \end{document} by appealing to functions of positive type and the structure theory of set addition.

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