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- W3099204558 abstract "We give a sufficient and necessary condition for a probability measure $mu$ on the real line to satisfy the logarithmic Sobolev inequality for convex functions. The condition is expressed in terms of the unique left-continuous and non-decreasing map transporting the symmetric exponential measure onto $mu$. The main tool in the proof is the theory of weak transport costs. As a consequence, we obtain dimension-free concentration bounds for the lower and upper tails of convex functions of independent random variables which satisfy the convex log-Sobolev inequality." @default.
- W3099204558 created "2020-11-23" @default.
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- W3099204558 date "2018-11-01" @default.
- W3099204558 modified "2023-09-25" @default.
- W3099204558 title "A characterization of a class of convex log-Sobolev inequalities on the real line" @default.
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- W3099204558 doi "https://doi.org/10.1214/17-aihp865" @default.
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