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Reflecting Poisson walks and dynamical universality in $p$-adic random matrix theory
- Publication Year :
- 2023
-
Abstract
- 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.<br />Comment: 49 pages, 3 figures. First version, comments welcome!
- Subjects :
- Mathematics - Probability
Mathematical Physics
Mathematics - Number Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2312.11702
- Document Type :
- Working Paper