Khinchin inequalities for uniforms on spheres with a deficit

TL;DR

This paper improves inequalities comparing moments of sums of uniform sphere vectors by introducing sharp constants and an optimal deficit term, especially relevant in high-dimensional settings.

Contribution

It provides the first sharp constants with a deficit term for Khinchin inequalities involving uniform vectors on spheres, enhancing existing bounds.

Findings

Derived sharp constants for moment inequalities

Introduced an optimal deficit term in high dimensions

Enhanced understanding of sum behavior of uniform sphere vectors

Abstract

We sharpen the moment comparison inequalities with sharp constants for sums of random vectors uniform on Euclidean spheres, providing a deficit term (optimal in high dimensions).