Moment estimates for chaoses generated by symmetric random variables with logarithmically convex tails

TL;DR

This paper provides precise two-sided estimates for random multilinear forms (chaoses) generated by independent symmetric variables with logarithmically convex tails, advancing understanding of their probabilistic behavior.

Contribution

It introduces exact two-sided estimates for chaoses with symmetric variables having logarithmically convex tails, a novel class of tail behavior.

Findings

Estimates are tight up to constants depending only on chaos order

Applicable to a broad class of symmetric random variables

Enhances understanding of chaos behavior with convex tail distributions

Abstract

We derive two-sided estimates for random multilinear forms (random chaoses) generated by independent symmetric random variables with logarithmically concave tails. Estimates are exact up to multiplicative constants depending only on the order of chaos.