Local Tail Bounds for Polynomials on the Discrete Cube

Bo’az Klartag; Sasha Sodin

doi:10.1007/978-3-031-26300-2_7

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 proceeding › Chapter › peer-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 language	English
Title of host publication	Geometric Aspects of Functional Analysis
Subtitle of host publication	Israel Seminar (GAFA) 2020-2022
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	223-230
Number of pages	8
DOIs	https://doi.org/10.1007/978-3-031-26300-2_7
State	Published - 2023
Externally published	Yes

Publication series

Name	Lecture Notes in Mathematics
Volume	2327
ISSN (Print)	0075-8434
ISSN (Electronic)	1617-9692

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

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10.1007/978-3-031-26300-2_7

Cite this

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Local Tail Bounds for Polynomials on the Discrete Cube

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