Limit theorems in free probability theory. I

DOI10.1214/009117907000000051zbMath1157.46037arXivmath/0602219OpenAlexW2064793276MaRDI QIDQ2468421

Friedrich Götze, Gennadiy P. Chistyakov

Publication date: 22 January 2008

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0602219

zbMATH Keywords

limit theoremsCauchy transformsfree convolutionsfree random variables

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Characteristic functions; other transforms (60E10) Free probability and free operator algebras (46L54)

Related Items (29)

Approximation of Free Convolutions by Free Infinitely Divisible Laws ⋮ Limit theorems in bi-free probability theory ⋮ A Berry-Esseen type limit theorem for Boolean convolution ⋮ Precise asymptotics of weighted sequences and their applications ⋮ Uniform convergence and the free central limit theorem ⋮ Asymptotic expansions in the CLT in free probability ⋮ Two-state free Brownian motions ⋮ Berry-Esseen bounds for the multivariate ℬ-free CLT and operator-valued matrices ⋮ Faster convergence in the free central limit theorem ⋮ On Boolean selfdecomposable distributions ⋮ Limit theorems in free probability theory II ⋮ Rates of convergence in the free central limit theorem ⋮ Free infinite divisibility of free multiplicative mixtures of the Wigner distribution ⋮ On a surprising relation between the Marchenko-Pastur law, rectangular and square free convolutions ⋮ Limit theorems for free multiplicative convolutions ⋮ On the supports of measures in free multiplicative convolution semigroups ⋮ The arithmetic of distributions in free probability theory ⋮ Limit theorems in free probability theory. I ⋮ Convergence rates for weighted sums in noncommutative probability space ⋮ Noncommutative probability and multiplicative cascades ⋮ Homomorphisms relative to additive convolutions and max-convolutions: Free, boolean and classical cases ⋮ Noncommutative Baum--Katz theorems ⋮ Nonuniversality of fluctuations of outliers for Hermitian polynomials in a complex Wigner matrix and a spiked diagonal matrix ⋮ Free Infinitely Divisible Approximations of n-Fold Free Convolutions ⋮ Convergence and asymptotic approximations to universal distributions in probability ⋮ Non-crossing partitions ⋮ On a Berry-Esseen type limit theorem for Boolean convolution ⋮ Monotone increment processes, classical Markov processes, and Loewner chains ⋮ An operad of non-commutative independences defined by trees

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