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arXiv · 1208.1125

Concentration of measures supported on the cube

Bo'az Klartag
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Abstract

We prove a log-Sobolev inequality for a certain class of log-concave measures in high dimension. These are the probability measures supported on the unit cube in R^n whose density takes the form exp(-H) where the function H is assumed to be convex (but not strictly convex) with bounded pure second derivatives. Our argument relies on a transportation-cost inequality a la Talagrand.

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Bo'az Klartag. 2012-12-17. Concentration of measures supported on the cube. https://arxiv.org/abs/1208.1125

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