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Concentration of measures supported on the cube

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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 [0, 1]n ⊂ ℝn whose density takes the form exp(−ψ), where the function ψ is assumed to be convex (but not strictly convex) with bounded pure second derivatives. Our argument relies on a transportation-cost inequality á la Talagrand.

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Authors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, Tel Aviv, 69978, Israel

    Bo’az Klartag

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  1. Bo’az Klartag
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Correspondence to Bo’az Klartag.

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In memory of Joram Lindenstrauss

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Klartag, B. Concentration of measures supported on the cube. Isr. J. Math. 203, 59–80 (2014). https://doi.org/10.1007/s11856-013-0072-1

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  • DOI: https://doi.org/10.1007/s11856-013-0072-1

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