Sums of Commutators in Free Probability
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arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866916265269919744 |
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| author | Ejsmont, Wiktor Lehner, Franz |
| author_facet | Ejsmont, Wiktor Lehner, Franz |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2002_06051 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Sums of Commutators in Free Probability Ejsmont, Wiktor Lehner, Franz Operator Algebras Combinatorics 46L54, 62E10 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. |
| title | Sums of Commutators in Free Probability |
| topic | Operator Algebras Combinatorics 46L54, 62E10 |
| url | https://arxiv.org/abs/2002.06051 |