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.
Original language | English |
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Article number | 108791 |
Journal | Journal of Functional Analysis |
Volume | 280 |
Issue number | 2 |
DOIs | |
Publication status | Published - 15 Jan 2021 |
Keywords
- Cancellation of free cumulants
- Commutator
- Free infinite divisibility
ASJC Scopus subject areas
- Analysis