An ergodic theorem for permanents of oblong matrices

Abstract

We form a sequence of oblong matrices by evaluating an integrable vector-valued function along the orbit of an ergodic dynamical system. We obtain an almost sure asymptotic result for the permanents of those matrices. We also give an application to symmetric means.

We were informed by the referee that our Theorem 1 is a particular case of a 1996 result of Aaronson, Burton, Dehling, Gilat, Hill, and Weiss. So this will become a permanent preprint