Reflecting Poisson walks and dynamical universality in p-adic random matrix theory
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 GLn(Zp)-invariant matrix distributions under weak universality hypotheses, with no spatial rescaling.
Fields of Study & Subjects
Topological and Geometric Data Analysis
advanced mathematical theories
Advanced Algebra and Geometry
Publication details
- Journal / source
- The Annals of Probability
- Volume
- 54
- Issue
- 5
- Pages
- 2568–2625
- Publication date
- 28 August 2026
- Language
- EN