Second Order Concentration via Logarithmic Sobolev Inequalities

TL;DR

This paper develops advanced concentration inequalities using second order difference operators and derivatives, improving understanding of measure concentration in discrete and statistical settings.

Contribution

It introduces second order concentration bounds based on second order difference operators and derivatives, extending classical measure concentration results.

Findings

Sharpened concentration bounds for functions on the discrete cube

Applications to stochastic Hoeffding expansions in statistics

Analysis of linear eigenvalue statistics in random matrix theory

Abstract

We show sharpened forms of the concentration of measure phenomenon centered at first order stochastic expansions. The bound are based on second order difference operators and second order derivatives. Applications to functions on the discrete cube and stochastic Hoeffding type expansions in mathematical statistics are studied as well as linear eigenvalue statistics in random matrix theory.