Log-concave measures

Details Log-concave measures Log-concave measures

2010-05-27

arxiv.org/abs/1005.5127v1

TWMS Journal of Pure and Applied Mathematics, Vol. 1, No.1, p. 92-105, 2010

Mathematics

Probability

Scientific paper

We study the log-concave measures, their characterization via the Pr\'ekopa-Leindler property and also define a subset of it whose elements are called super log-concave measures which have the property of satisfying a logarithmic Sobolev inequality. We give some results about their stability. Certain relations with measure transportation of Monge-Kantorovitch and the Monge-Amp\'ere equation are also indicated with applications.

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