Reflecting Poisson walks and dynamical universality in p-adic random matrix theory

2023/12/18 by Van Peski, Roger · 3 citations
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Number Theory (math.NT) #Probability (math.PR)

paper · doi:10.48550/arxiv.2312.11702

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 GL_n(ℤ_p)-invariant matrix distributions under weak universality hypotheses, with no spatial rescaling.

Cited by

• Geometry-induced criticality in p-adic scaling limits of random walks
• Cohen-Lenstra flag universality for random matrix products
• The fluctuations of the mod p rank of triangular matrices

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