Mark Kac introduced a method for calculating the distribution of the integral Av=[integral operator]0Tv(Xt) dt for a function v of a Markov process (Xt, t[greater-or-equal, slanted]0) and a suitable random time T, which yields the Feynman-Kac formula for the moment-generating function of Av. We...

We consider the elementary divisors and determinant of a uniformly distributed nxn random matrix with entries in the ring of integers of an arbitrary local field. We show that the sequence of elementary divisors is in a simple bijective correspondence with a Markov chain on the non-negative...