2022/10/16 by Hoi H. Nguyen, Melanie Matchett Wood, Nguyen, Hoi H. +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Probability (math.PR) #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.2210.08526
openalex publication_date 2022/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.