Asymptotic Expansions in the CLT in Free Probability

2011/09/22 by G. P. Chistyakov, Chistyakov, G. P., F. Götze +1 · 1 citation
Mathematics · #46L50 #60E07 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:46L50 #msc:60E07

paper · pdf · doi:10.48550/arxiv.1109.4844

This version contains some small corrections and reformulations

arxiv created 2011/12/21 · arxiv updated 2011/12/22

Abstract

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.

Cited by

• Rates of convergence in the Free Multiplicative Central Limit Theorem

Related

• Edgeworth-type expansion in the entropic free CLT
• Asymptotic Expansions in Free Limit Theorems
• Rate of Convergence in the entropic free CLT
• Limit Theorems in Free Probability Theory I
• Fisher information and the central limit theorem