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Paper detail

Stability of Poincar{é} constant

We study stability of the sharp Poincar{é} 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{é} 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.

preprint2022arXivOpen access
Jordan Serres
math.PRmath.SPmath.CA
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