Free probability of type <i>B</i>: analytic interpretation and applications

DOI10.1353/ajm.2012.0003zbMath1253.46070arXiv0903.2721OpenAlexW3099770389MaRDI QIDQ2879629

Dimitri Shlyakhtenko, Serban Teodor Belinschi

Publication date: 29 March 2012

Published in: American Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0903.2721

zbMATH Keywords

hyperoctahedral groupfree probabilityinfinitesimal freenesstype B non-crossing partitions

Mathematics Subject Classification ID

Free probability and free operator algebras (46L54) Noncommutative probability and statistics (46L53)

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Finite free cumulants: Multiplicative convolutions, genus expansion and infinitesimal distributions ⋮ A unified approach to infinitesimal freeness with amalgamation ⋮ The double Fock space of type B ⋮ Asymptotic infinitesimal freeness with amalgamation for Haar quantum unitary random matrices ⋮ Multiplicative and semi-multiplicative functions on non-crossing partitions, and relations to cumulants ⋮ Free probability for pairs of faces. I ⋮ Relations between infinitesimal non-commutative cumulants ⋮ Star-cumulants of free unitary Brownian motion ⋮ Infinitesimal non-crossing cumulants and free probability of type B ⋮ Fock space associated to Coxeter groups of type B ⋮ Free probability of type B and asymptotics of finite-rank perturbations of random matrices ⋮ Non‐crossing annular pairings and the infinitesimal distribution of the<scp>goe</scp> ⋮ A construction which relates $c$-freeness to infinitesimal freeness ⋮ On operator-valued infinitesimal Boolean and monotone independence

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