Boolean Cumulants and Subordination in Free Probability
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866916265263628288 |
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| author | Lehner, Franz Szpojankowski, Kamil |
| author_facet | Lehner, Franz Szpojankowski, Kamil |
| contents | We study subordination of free convolutions. We prove that for free random variables $X,Y$ and a Borel function $f$ the conditional expectation $E_φ\left[ (z-X-f(X)Yf^*(X))^{-1}| X\right]$, is a resolvent again. This result allows explicit calculation of the distribution of $X+f(X)Yf^*(X)$. The main tool is a formula for conditional expectations in terms of Boolean cumulant transforms, generalizing subordination formulas for free additive and multiplicative convolutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1907_11442 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Boolean Cumulants and Subordination in Free Probability Lehner, Franz Szpojankowski, Kamil Operator Algebras Probability We study subordination of free convolutions. We prove that for free random variables $X,Y$ and a Borel function $f$ the conditional expectation $E_φ\left[ (z-X-f(X)Yf^*(X))^{-1}| X\right]$, is a resolvent again. This result allows explicit calculation of the distribution of $X+f(X)Yf^*(X)$. The main tool is a formula for conditional expectations in terms of Boolean cumulant transforms, generalizing subordination formulas for free additive and multiplicative convolutions. |
| title | Boolean Cumulants and Subordination in Free Probability |
| topic | Operator Algebras Probability |
| url | https://arxiv.org/abs/1907.11442 |