English

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

R2 v1 2026-06-28T03:44:47.432Z