An ergodic theorem for permanents of oblong matrices

TL;DR

This paper establishes an almost sure asymptotic theorem for the permanents of oblong matrices generated by ergodic dynamical systems, with applications to symmetric means.

Contribution

It introduces a new ergodic theorem for permanents of matrices formed from dynamical systems, extending the understanding of asymptotic behavior of such matrix invariants.

Findings

Almost sure asymptotic behavior of matrix permanents

Application to symmetric means

Extension of ergodic theorems to matrix permanents

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.