A Free Analogue of Shannon's Problem on Monotonicity of Entropy

Details A Free Analogue of Shannon's Problem on Monotonicity of Entropy A Free Analogue of Shannon's Problem on Monotonicity of Entropy

2005-10-05

arxiv.org/abs/math/0510103v1

Mathematics

Operator Algebras

Scientific paper

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.

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