Local and global universality of random matrix cokernels
Probability
2022-10-18 v1 Combinatorics
Number Theory
Abstract
In this paper we study the cokernels of various random integral matrix models, including random symmetric, random skew-symmetric, and random Laplacian matrices. We provide a systematic method to establish universality under very general randomness assumption. Our highlights include both local and global universality of the cokernel statistics of all these models. In particular, we find the probability that a sandpile group of an Erdos-Renyi random graph is cyclic, answering a question of Lorenzini from 2008.
Keywords
Cite
@article{arxiv.2210.08526,
title = {Local and global universality of random matrix cokernels},
author = {Hoi H. Nguyen and Melanie Matchett Wood},
journal= {arXiv preprint arXiv:2210.08526},
year = {2022}
}
Comments
68 pages