Frequently hypercyclic random vectors

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.

arXiv comment21 pages; results not valid for arbitrary F-spaces but for locally bounded or locally convex F-spaces