Frequently hypercyclic random vectors

TL;DR

This paper demonstrates that certain shift-like operators on sequence spaces possess frequently hypercyclic vectors with strongly mixing distributions, and applies these findings to chaotic weighted shifts and operators satisfying the Frequent Hypercyclicity Criterion.

Contribution

It introduces conditions under which shift-like operators have frequently hypercyclic vectors with strongly mixing distributions, extending previous results to chaotic weighted shifts and operators meeting the criterion.

Findings

Existence of frequently hypercyclic vectors with strongly mixing distributions for shift-like operators

Application to chaotic weighted shifts demonstrating their hypercyclicity

Recovery of Murillo and Peris's result for operators satisfying the Frequent Hypercyclicity Criterion

Abstract

We show that, under suitable conditions, an operator acting like a shift on some sequence space has a frequently hypercyclic random vector whose distribution is strongly mixing for the operator. This result will be applied to chaotic weighted shifts. We also apply it to every operator satisfying the Frequent Hypercyclicity Criterion, recovering a result of Murillo and Peris.