The Law of Large Numbers for the Free Multiplicative Convolution

DOI10.1007/978-3-642-39459-1_8zbMath1319.46045arXiv1211.4457OpenAlexW1516287220MaRDI QIDQ5244496

Sören Möller, Uffe Haagerup

Publication date: 27 March 2015

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.4457

zbMATH Keywords

free convolutionlaw of large numbersfree probabilityfree multiplicative law

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Free probability and free operator algebras (46L54)

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A phase transition for tails of the free multiplicative convolution powers ⋮ A survey on the effects of free and Boolean convolutions on Cauchy-Stieltjes kernel families ⋮ Some properties of the free stable distributions ⋮ \(k\)-divisible random variables in free probability ⋮ Beyond islands: a free probabilistic approach ⋮ Local universality in biorthogonal Laguerre ensembles ⋮ Explicit free multiplicative law of large numbers ⋮ Law of large numbers for roots of finite free multiplicative convolution of polynomials ⋮ Max-convolution semigroups and extreme values in limit theorems for the free multiplicative convolution ⋮ Continuity and growth of free multiplicative convolution semigroups ⋮ A Fuss-type family of positive definite sequences ⋮ Classical scale mixtures of Boolean stable laws ⋮ Homomorphisms relative to additive convolutions and max-convolutions: Free, boolean and classical cases ⋮ On generating functions of Hausdorff moment sequences ⋮ Raney distributions and random matrix theory

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