Reflecting Poisson walks and dynamical universality in $p$-adic random matrix theory
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908760510824448 |
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| author | Van Peski, Roger |
| author_facet | Van Peski, Roger |
| contents | We prove dynamical local limits for the singular numbers of $p$-adic random matrix products at both the bulk and edge. The limit object which we construct, the reflecting Poisson sea, may thus be viewed as a $p$-adic analogue of line ensembles appearing in classical random matrix theory. However, in contrast to those it is a discrete space Poisson-type particle system with only local reflection interactions and no obvious determinantal structure. The limits hold for any $\mathrm{GL}_n(\mathbb{Z}_p)$-invariant matrix distributions under weak universality hypotheses, with no spatial rescaling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_11702 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Reflecting Poisson walks and dynamical universality in $p$-adic random matrix theory Van Peski, Roger Probability Mathematical Physics Number Theory We prove dynamical local limits for the singular numbers of $p$-adic random matrix products at both the bulk and edge. The limit object which we construct, the reflecting Poisson sea, may thus be viewed as a $p$-adic analogue of line ensembles appearing in classical random matrix theory. However, in contrast to those it is a discrete space Poisson-type particle system with only local reflection interactions and no obvious determinantal structure. The limits hold for any $\mathrm{GL}_n(\mathbb{Z}_p)$-invariant matrix distributions under weak universality hypotheses, with no spatial rescaling. |
| title | Reflecting Poisson walks and dynamical universality in $p$-adic random matrix theory |
| topic | Probability Mathematical Physics Number Theory |
| url | https://arxiv.org/abs/2312.11702 |