Subadditivity of the log-Sobolev constant on convolutions

2025/08/27 by Courtade, Thomas A., Wang, Edric
#FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Information Theory (cs.IT) #Probability (math.PR)

paper · doi:10.48550/arxiv.2508.19648

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.

Citations

• Dimension-free log-Sobolev inequalities for mixture distributions
• Bounds on the Poincaré constant for convolution measures
• Existence of Stein Kernels under a Spectral Gap, and Discrepancy Bound

Related

• On the log-Sobolev constant of log-concave measures
• Elementary proof of logarithmic Sobolev inequalities for Gaussian convolutions on ℝ
• Bounds on the Poincaré constant for convolution measures
• Log-concavity and strong log-concavity: a review
• Modified log-Sobolev inequalities for strongly log-concave distributions