TY - CHAP

T1 - Local Tail Bounds for Polynomials on the Discrete Cube

AU - Klartag, Bo’az

AU - Sodin, Sasha

N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85175035198&partnerID=8YFLogxK

U2 - 10.1007/978-3-031-26300-2_7

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

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AN - SCOPUS:85175035198

T3 - Lecture Notes in Mathematics

SP - 223

EP - 230

BT - Lecture Notes in Mathematics

PB - Springer Science and Business Media Deutschland GmbH

ER -