Concentration of the information in data with log-concave distributions

Details Concentration of the information in data with log-concave distributions Concentration of the information in data with log-concave distributions

2010-12-25

arxiv.org/abs/1012.5457v1

The Annals of Probability, Vol. 39, No. 4, pp. 1528-1543, 2011

Mathematics

Probability

18 pages

Scientific paper

10.1214/10-AOP592

A concentration property of the functional $-\log f(X)$ is demonstrated, when
a random vector $X$ has a log-concave density $f$ on $\R^n$. This concentration
property implies in particular an extension of the Shannon-McMillan-Breiman
strong ergodic theorem to the class of discrete-time stochastic processes with
log-concave marginals.

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