Local Tail Bounds for Polynomials on the Discrete Cube

Bo’az Klartag, Sasha Sodin*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

Let P be a polynomial of degree d in independent Bernoulli random variables which has zero mean and unit variance. The Bonami hypercontractivity bound implies that the probability that | P| > t decays exponentially in t2 d. Confirming a conjecture of Keller and Klein, we prove a local version of this bound, providing an upper bound on the difference between the e r and the e r 1 quantiles of P.

Original languageEnglish
Title of host publicationLecture Notes in Mathematics
PublisherSpringer Science and Business Media Deutschland GmbH
Pages223-230
Number of pages8
DOIs
StatePublished - 2023
Externally publishedYes

Publication series

NameLecture Notes in Mathematics
Volume2327
ISSN (Print)0075-8434
ISSN (Electronic)1617-9692

Funding

FundersFunder number
Leverhulme TrustPLP-2020-064
Royal SocietyWM170012
Israel Science Foundation

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