Abstract
We study stability of the sharp Poincaré constant of the invariant probability measure of a reversible diffusion process satisfying some natural conditions. The proof is based on the spectral interpretation of Poincaré inequalities and Stein’s method. In particular, these results are applied to gamma distributions, to the Brownian motion on spheres and to the Brascamp-Lieb inequality for one-dimensional log-concave measures.
Acknowledgments
I would like to thank my PhD advisors Franck Barthe and Max Fathi for their availability and all their fruitful advice.
Citation
Serres Jordan. "Stability of the Poincaré constant." Bernoulli 29 (2) 1297 - 1320, May 2023. https://doi.org/10.3150/22-BEJ1499