Let $A$ be a random $n$ by $n$ matrix over $\mathbb{Z}_p$ which is
equidistributed with respect to the Haar measure. Friedman and Washington
proved that the distribution of the cokernel of $A$ follows the Cohen-Lenstra
distribution. In this talk, we introduce three possible ways to generalize
their work. In particular, we discuss the following results:
1. Joint distribution of the cokernels $cok(P_1(A)), ... , cok(P_l(A))$ for
polynomials $P_1(t), ... , P_l(t) \in \mathbb{Z}_p[t]$ under some mild conditions
2. Universality of the cokernel of a random Hermitian matrix over the ring
of integers of a quadratic extension of $\mathbb{Q}_p$.
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Meeting ID: 864 8102 3050
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