* Title : Sharp threshold for universality of cokernels of random p-adic matrices

* Speaker : Jungin Lee (Ajou University)

* Abstract : 

In this talk, we present a sharp universality theorem for cokernels of classical random matrix models over the ring of p-adic integers Zp. Let A(n) be an n×n random matrix over Zp whose entries satisfy a balanced condition at scale (clogn)/n. For nonsymmetric, symmetric, and alternating random matrix models, we prove that for every c>1, the cokernel of A(n) converges in distribution to the corresponding universal limit as n->∞. The universality fails at the critical scale c=1, showing that the threshold c>1 is sharp. This improves earlier universality results, which required much stronger balanced assumptions. We also improve the universality result for sandpile groups of Erdős–Rényi random graphs. The proof is based on a unified framework that treats all symmetry types simultaneously. This talk is based on the joint work with Jiwan Jung and Myungjun Yu.