From Ball's cube slicing inequality to Khinchin-type inequalities for negative moments

TL;DR

This paper extends Ball's cube slicing inequality to establish a sharp comparison between negative and second moments for sums of independent uniform variables, contributing to the understanding of moment inequalities.

Contribution

It introduces a new inequality linking negative moments to the second moment for uniform sums, generalizing Ball's cube slicing inequality.

Findings

Established a sharp moment comparison inequality for negative and second moments.

Extended Ball's cube slicing inequality to a broader class of random variables.

Provided theoretical bounds for sums of independent uniform variables.

Abstract

We establish a sharp moment comparison inequality between an arbitrary negative moment and the second moment for sums of independent uniform random variables, which extends Ball's cube slicing inequality.