[HG_A] Sharp threshold for universality of cokernels of random matrices over the p-adic integers
ABSTRACT
In this talk, we present a sharp universality theorem for cokernels of classical random matrix models over the ring of p-adic integers Z_p. For nonsymmetric, symmetric, and alternating random matrices over Z_p satisfying a balanced condition at scale (clogn)/n with c>1, we prove that the cokernel converges in distribution to the corresponding universal limit as n->∞. Universality fails at the critical scale c=1, showing that the threshold c>1 is sharp. 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 joint work with Jiwan Jung and Myungjun Yu.
