Sums of Commutators in Free Probability
Operator Algebras
2024-05-31 v2 Combinatorics
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
Cite
@article{arxiv.2002.06051,
title = {Sums of Commutators in Free Probability},
author = {Wiktor Ejsmont and Franz Lehner},
journal= {arXiv preprint arXiv:2002.06051},
year = {2024}
}
Comments
21 pages; numerous improvements suggested by an anonymous referee; figures changed to black and white (color can be switched on in latex file); limit theorems moved to separate paper arXiv:2004.02679