Stability of Poincar{\'e} constant
Classical Analysis and ODEs
2022-02-04 v2 Probability
Spectral Theory
Abstract
We study stability of the sharp Poincar{\'e} constant of the invariant probability measure of a reversible diffusion process satisfying some natural conditions. The proof is based on the spectral interpretation of Poincar{\'e} inequalities and Stein's method. In particular, these results are applied to the gamma distributions and to strictly log-concave measures in dimension one, giving stability for Brascamp-Lieb inequalities.
Keywords
Cite
@article{arxiv.2105.12607,
title = {Stability of Poincar{\'e} constant},
author = {Jordan Serres},
journal= {arXiv preprint arXiv:2105.12607},
year = {2022}
}