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arXiv · 2105.12607

Stability of Poincar{\'e} constant

Jordan Serres
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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.

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Jordan Serres. 2021-05-26. Stability of Poincar{\'e} constant. https://arxiv.org/abs/2105.12607

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