Comparison of moments of Rademacher chaoses

TL;DR

This paper demonstrates that complex hypercontractivity provides improved constants over real hypercontractivity in inequalities related to the moments of Rademacher chaoses, which are homogeneous polynomials on the discrete cube.

Contribution

It introduces the use of complex hypercontractivity to obtain sharper constants in moment comparison inequalities for Rademacher chaoses.

Findings

Complex hypercontractivity yields better constants than real hypercontractivity.

Improved inequalities for moments of Rademacher chaoses.

Enhanced understanding of hypercontractivity in discrete polynomial settings.

Abstract

We show that complex hypercontractivity gives better constants than real hypercontractivity in comparison inequalities for (low) moments of Rademacher chaoses (homogeneous polynomials on the discrete cube).