Variations and extensions of the Gaussian concentration inequality, Part II

TL;DR

This paper extends Gaussian concentration inequalities to heavy-tailed distributions, providing bounds for functions of independent Weibull or power-type variables, advancing the understanding of concentration phenomena in non-sub-Gaussian settings.

Contribution

It introduces new concentration inequalities for functions of heavy-tailed random vectors, expanding the applicability of Gaussian concentration techniques.

Findings

Derived concentration bounds for heavy-tailed variables

Applicable to functions with local Lipschitz continuity

Part of a series on Gaussian concentration extensions

Abstract

We prove concentration inequalities for $f\left( X\right) $ about its median, where $X$ is a random vector in $\mathbb{R}^n$ with independent heavy tailed coordinates of Weibull or power type, and $f:\mathbb{R}^n\rightarrow\mathbb{R}$ is a locally Lipschitz function. This paper is part of a series of four papers, Part I, Part II and two supporting papers. It can be read independently of Part I.