Restricted Khinchine inequality

TL;DR

This paper establishes a new Khintchine inequality for sums of Rademacher variables conditioned on their sum being zero, and applies it to derive a novel tail bound for hypergeometric distributions.

Contribution

It introduces a restricted Khintchine inequality under a specific sum constraint and demonstrates its use in deriving tail bounds for hypergeometric variables.

Findings

Proved a Khintchine inequality for Rademacher sums with zero sum constraint.

Derived a new tail bound for hypergeometric random variables.

Showed the inequality's application in probabilistic bounds.

Abstract

We prove a Khintchine type inequality under the assumption that the sum of Rademacher random variables equals zero. As an application we show a new tail-bound for a hypergeometric random variable.