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In this paper we study the cokernels of various random integral matrixmodels, including random symmetric, random skew-symmetric, and random Laplacianmatrices. We provide a systematic method to establish universality under verygeneral randomness assumption. Our highlights include both local and globaluniversality of the cokernel statistics of all these models. In particular, wefind the probability that a sandpile group of an Erdos-Renyi random graph iscyclic, answering a question of Lorenzini from 2008.

Local and global universality of random matrix cokernels