A Free Analogue of Shannon's Problem on Monotonicity of Entropy
Operator Algebras
2007-05-23 v1 Probability
Abstract
We prove a free probability analog of a result of Artstein-Bally-Barthez-Naor. In particualar we prove that if X_{1},X_{2},... are freely independent identically distributed random variables, then the free entropy chi(X_{1}+...+X_{n}/\sqrt{n}) is monotone increasing for all n. Our proof also leads to a slight simplification of the original argument in the classical case.
Cite
@article{arxiv.math/0510103,
title = {A Free Analogue of Shannon's Problem on Monotonicity of Entropy},
author = {D. Shlyakhtenko},
journal= {arXiv preprint arXiv:math/0510103},
year = {2007}
}