HWI inequalities in discrete spaces via couplings
Probability
2023-12-05 v1 Functional Analysis
Abstract
HWI inequalities are interpolation inequalities relating entropy, Fisher information and optimal transport distances. We adapt an argument of Y. Wu for proving the Gaussian HWI inequality via a coupling argument to the discrete setting, establishing new interpolation inequalities for the discrete hypercube and the discrete torus. In particular, we obtain an improvement of the modified logarithmic Sobolev inequality for the discrete hypercube of Bobkov and Tetali.
Keywords
Cite
@article{arxiv.2312.01368,
title = {HWI inequalities in discrete spaces via couplings},
author = {Thomas A. Courtade and Max Fathi},
journal= {arXiv preprint arXiv:2312.01368},
year = {2023}
}
Comments
11 pages, comments welcome