Center of mass distribution of the Jacobi unitary ensembles: Painleve V, asymptotic expansions
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2018
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| _version_ | 1866912040516321280 |
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| author | Zhan, Longjun Blower, Gordon Chen, Yang Zhu, Mengkun |
| author_facet | Zhan, Longjun Blower, Gordon Chen, Yang Zhu, Mengkun |
| contents | In this paper, we study the probability density function, $\mathbb{P}(c,α,β, n)\,dc$, of the center of mass of the finite $n$ Jacobi unitary ensembles with parameters $α\,>-1$ and $β>-1$; that is the probability that ${\rm tr}M_n\in(c, c+dc),$ where $M_n$ are $n\times n$ matrices drawn from the unitary Jacobi ensembles. We first compute the exponential moment generating function of the linear statistics $\sum_{j=1}^{n}\,f(x_j):=\sum_{j=1}^{n}x_j,$ denoted by $\mathcal{M}_f(λ,α,β,n)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1801_07454 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Center of mass distribution of the Jacobi unitary ensembles: Painleve V, asymptotic expansions Zhan, Longjun Blower, Gordon Chen, Yang Zhu, Mengkun Classical Analysis and ODEs 34M55, 33C45 In this paper, we study the probability density function, $\mathbb{P}(c,α,β, n)\,dc$, of the center of mass of the finite $n$ Jacobi unitary ensembles with parameters $α\,>-1$ and $β>-1$; that is the probability that ${\rm tr}M_n\in(c, c+dc),$ where $M_n$ are $n\times n$ matrices drawn from the unitary Jacobi ensembles. We first compute the exponential moment generating function of the linear statistics $\sum_{j=1}^{n}\,f(x_j):=\sum_{j=1}^{n}x_j,$ denoted by $\mathcal{M}_f(λ,α,β,n)$. |
| title | Center of mass distribution of the Jacobi unitary ensembles: Painleve V, asymptotic expansions |
| topic | Classical Analysis and ODEs 34M55, 33C45 |
| url | https://arxiv.org/abs/1801.07454 |