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Stability of Poincar{\'e} constant

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arxiv 2105.12607 v2 pith:ODESVXF7 submitted 2021-05-26 math.CA math.PRmath.SP

Jordan Serres (IMT) This is my paper · ORCID
classification math.CAmath.PRmath.SP
keywords poincarstabilityconstantinequalitiesappliedbrascamp-liebconditionsdiffusion
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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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  1. Quantitative stability in distribution for the Sobolev inequality under curvature dimension condition

    math.AP 2026-07 accept novelty 7.0 of 10

    In CD(N-1,N) spaces with near-sharp Sobolev constant, the pushforward measure of any almost-extremal is close in Wasserstein distance to an Aubin-Talenti bubble distribution, with sharp √ε rate.

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