Asymptotic Expansions in the CLT in Free Probability

Details Asymptotic Expansions in the CLT in Free Probability Asymptotic Expansions in the CLT in Free Probability

2011-09-22

arxiv.org/abs/1109.4844v2

Mathematics

Probability

This version contains some small corrections and reformulations

Scientific paper

We prove Edgeworth type expansions for distribution functions of sums of free
random variables under minimal moment conditions. The proofs are based on the
analytic definition of free convolution. We apply these results to the
expansion of densities to derive expansions for the free entropic distance of
sums to the Wigner law.

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