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The Smith normal form of a polynomial of a random integral matrix (Gilyoung Cheong, UC Irvine)
The Smith normal form of a polynomial of a random integral matrix (Gilyoung Cheong, UC Irvine)
Given a prime p, let P(t) be a non-constant monic polynomial in t over the ring of p-adic integers. Let X(n) be an n x n uniformly random (0,1)-matrix over the same ring. We compute the asymptotic distribution of the cokernel of P(X(n)) as n goes to infinity. When P(t) is square-free modulo p, this […]