Sums of commutators in free probability

Wiktor Ejsmont; Franz Lehner

doi:10.1016/j.jfa.2020.108791

Sums of commutators in free probability

Wiktor Ejsmont^*, Franz Lehner

^*Korrespondierende/r Autor/-in für diese Arbeit

Institut für Diskrete Mathematik (5050)

Publikation: Beitrag in einer Fachzeitschrift › Artikel › Begutachtung

Abstract

We study the linear span of commutators of free random variables and show that these are the only quadratic forms which satisfy the following equivalent properties: • preservation free infinite divisibility, • free and strong cancellation of odd cumulants, • symmetric distribution for any free family. The main combinatorial tool is an involution on non-crossing partitions.

Originalsprache	englisch
Aufsatznummer	108791
Fachzeitschrift	Journal of Functional Analysis
Jahrgang	280
Ausgabenummer	2
DOIs	https://doi.org/10.1016/j.jfa.2020.108791
Publikationsstatus	Veröffentlicht - 15 Jan. 2021

ASJC Scopus subject areas

Analyse

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10.1016/j.jfa.2020.108791

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title = "Sums of commutators in free probability",

abstract = "We study the linear span of commutators of free random variables and show that these are the only quadratic forms which satisfy the following equivalent properties: • preservation free infinite divisibility, • free and strong cancellation of odd cumulants, • symmetric distribution for any free family. The main combinatorial tool is an involution on non-crossing partitions.",

keywords = "Cancellation of free cumulants, Commutator, Free infinite divisibility",

author = "Wiktor Ejsmont and Franz Lehner",

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AB - We study the linear span of commutators of free random variables and show that these are the only quadratic forms which satisfy the following equivalent properties: • preservation free infinite divisibility, • free and strong cancellation of odd cumulants, • symmetric distribution for any free family. The main combinatorial tool is an involution on non-crossing partitions.

KW - Cancellation of free cumulants

KW - Commutator

KW - Free infinite divisibility

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U2 - 10.1016/j.jfa.2020.108791

DO - 10.1016/j.jfa.2020.108791

M3 - Article

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Sums of commutators in free probability

Abstract

ASJC Scopus subject areas

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