PROBABILITY MASS OF RADEMACHER SUMS BEYOND ONE STANDARD DEVIATION

Vojtech Dvorak, Ohad Klein

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Let a1, . . ., an \in \BbbR satisfy \sumi a2i = 1, and let \varepsilon 1, . . ., \varepsilon n be uniformly random \pm 1 signs and X = \sum ni=1 ai\varepsilon i. It is conjectured that X = \sum ni=1 ai\varepsilon i has Pr[X \geq 1] \geq 7/64. The best lower bound so far is 1/20, due to Oleszkiewicz. In this paper we improve this to Pr[X \geq 1] \geq 6/64.

Original languageEnglish
Pages (from-to)2393-2410
Number of pages18
JournalSIAM Journal on Discrete Mathematics
Volume36
Issue number3
DOIs
StatePublished - 2022

Bibliographical note

Publisher Copyright:
© 2022 Society for Industrial and Applied Mathematics.

Keywords

  • Rademacher sums
  • anti-concentration
  • combinatorial probability

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