A concentration property of the functional - log f(X) is demonstrated, when a random vector X has a log-concave density f on Rn. 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.
- Asymptotic equipartition property
- Log-concave distributions
- Shannon-Mcmillan-Breiman theorem