On the improvement of concavity of convex measures

Marsiglietti, Arnaud

doi:10.1090/proc/12694

On the improvement of concavity of convex measures
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Proc. Amer. Math. Soc. 144 (2016), 775-786 Request permission

Abstract:

We prove that a general class of measures, which includes $\log$-concave measures, is $\frac {1}{n}$-concave according to the terminology of Borell, with additional assumptions on the measures or on the sets, such as symmetries. This generalizes results of Gardner and Zvavitch published in 2010.

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