The Distribution of Polynomials in Monotone Independent Elements
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914788073799680 |
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| author | Banna, Marwa Tseng, Pei-Lun |
| author_facet | Banna, Marwa Tseng, Pei-Lun |
| contents | Building on the work of Arizmendi and Celestino (2021), we derive the $*$-distributions of polynomials in monotone independent and infinitesimally monotone independent elements. For non-zero complex numbers $α$ and $β$, we derive explicitly the $*$-distribution of $p_{α,β}=αab + βba$ whenever $a$ and $b$ are monotone or infinitesimally monotone independent elements. This encompasses both cases of the commutator and anti-commutator. This approach can be pushed to study more general polynomials. As applications, we derive the limiting distribution with respect to the partial trace of polynomials in a certain class of random matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_05979 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Distribution of Polynomials in Monotone Independent Elements Banna, Marwa Tseng, Pei-Lun Probability 46L53, 60B20 Building on the work of Arizmendi and Celestino (2021), we derive the $*$-distributions of polynomials in monotone independent and infinitesimally monotone independent elements. For non-zero complex numbers $α$ and $β$, we derive explicitly the $*$-distribution of $p_{α,β}=αab + βba$ whenever $a$ and $b$ are monotone or infinitesimally monotone independent elements. This encompasses both cases of the commutator and anti-commutator. This approach can be pushed to study more general polynomials. As applications, we derive the limiting distribution with respect to the partial trace of polynomials in a certain class of random matrices. |
| title | The Distribution of Polynomials in Monotone Independent Elements |
| topic | Probability 46L53, 60B20 |
| url | https://arxiv.org/abs/2311.05979 |