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- W2897974298 abstract "The goal of this paper is to push forward the study of those properties of log-concave measures that help to estimate their Poincaré constant. First we revisit E. Milman’s result (Invent Math 177:1–43, 2009) on the link between weak (Poincaré or concentration) inequalities and Cheeger’s inequality in the log-concave cases, in particular extending localization ideas and a result of Latala, as well as providing a simpler proof of the nice Poincaré (dimensional) bound in the unconditional case. Then we prove alternative transference principle by concentration or using various distances (total variation, Wasserstein). A mollification procedure is also introduced enabling, in the log-concave case, to reduce to the case of the Poincaré inequality for the mollified measure. We finally complete the transference section by the comparison of various probability metrics (Fortet-Mourier, bounded-Lipschitz, …) under a log-concavity assumption." @default.
- W2897974298 created "2018-10-26" @default.
- W2897974298 creator A5023809964 @default.
- W2897974298 creator A5051679487 @default.
- W2897974298 date "2020-01-01" @default.
- W2897974298 modified "2023-10-04" @default.
- W2897974298 title "On the Poincaré Constant of Log-Concave Measures" @default.
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- W2897974298 doi "https://doi.org/10.1007/978-3-030-36020-7_9" @default.
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