A Free Analogue of Shannon's Problem on Monotonicity of Entropy
Abstract
We prove a free probability analog of a result of Artstein-Bally-Barthez-Naor. In particualar we prove that if X1,X2,... are freely independent identically distributed random variables, then the free entropy chi(X1+...+Xn/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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