Subadditivity of the log-Sobolev constant on convolutions

TL;DR

This paper establishes a subadditivity inequality for log-Sobolev constants in convolution measures and demonstrates their monotonicity in the context of the central limit theorem.

Contribution

It introduces a general subadditivity inequality for log-Sobolev constants and proves their monotonic behavior in standardized convolutions.

Findings

Log-Sobolev constant is subadditive under convolution.

Monotonic increase of the log-Sobolev constant along standardized convolutions.

Supports the understanding of entropy and concentration in probability measures.

Abstract

We present a general subadditivity inequality for log-Sobolev constants of convolution measures. As a corollary, we show that the log-Sobolev constant is monotone along the sequence of standardized convolutions in the central limit theorem.