Improved one-sided deviation inequalities under regularity assumptions for product measures

TL;DR

This paper presents improved lower tail deviation inequalities for functions under product measures, utilizing semigroup interpolation, Harris's negative association, and hypercontractivity, under certain regularity and monotonicity conditions.

Contribution

It introduces novel lower tail deviation inequalities for product measures based on regularity and monotonicity assumptions, employing advanced probabilistic techniques.

Findings

Enhanced deviation inequalities for product measures

Applicable under regularity and monotonicity conditions

Utilizes semigroup interpolation and hypercontractive estimates

Abstract

This note is concerned with lower tail estimates for product measures. Some improved deviation inequalities are obtained for functions satisfying some regularity and monotonicity assumptions. The arguments are based on semigroup interpolation together with Harris's negative association inequality and hypercontractive estimates.