Joint distribution of the cokernels of random p-adic matrices

In this paper, we study the joint distribution of the cokernels of random p-adic matrices. Let p be a prime and let P-1(t), ... , P-l(t) ? Z(p)[t] be monic polynomials whose reductions modulo p in F-p[t] are distinct and irreducible. We determine the limit of the joint distribution of the cokernels cok(P-1(A)), ... , cok(P-l(A)) for a random n x n matrix A over Z(p) with respect to the Haar measure as n ? 8. By applying the linearization of a random matrix model, we also provide a conjecture which generalizes this result. Finally, we provide a sufficient condition that the cokernels cok(A) and cok(A + B-n) become independent as n ? 8, where B-n is a fixed n x n matrix over Z(p) for each n and A is a random n x n matrix over Z(p).