Work

Local limits in p$p$‐adic random matrix theory

Year: 2024

Type: article

Abstract: We study the distribution of singular numbers of products of certain classes of ‐adic random matrices, as both the matrix size and number of products go to simultaneously. In this limit, we prove convergence of the local statistics to a new random point configuration on , defined explicitly in terms of certain intricate mixed ‐series/exponential sums. This object may be viewed as a nontrivial ‐adic analogue of the interpolating distributions of Akemann–Burda–Kieburg, which generalize the sine and Airy kernels and govern limits of complex matrix products. Our proof uses new Macdonald process computations and holds for matrices with iid additive Haar entries, corners of Haar matrices from , and the ‐adic analogue of Dyson Brownian motion studied by the author ( https://arxiv.org/pdf/2309.02865 ).

Source: Proceedings of the London Mathematical Society

DOI: 10.1112/plms.12626

Author: Roger Van Peski

Institution: KTH Royal Institute of Technology

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,520

Funders: National Science Foundation, European Research Council