Common frequently hypercyclic random vectors

TL;DR

This paper investigates the existence of common frequently hypercyclic vectors for families of weighted backward shifts on ll_p spaces, introducing probabilistic methods and applying them to polynomial families of such shifts.

Contribution

It develops a general probabilistic criterion for the existence of common frequently hypercyclic vectors and applies it to polynomial families of weighted backward shifts.

Findings

Established a criterion for the existence of common frequently hypercyclic vectors.

Provided conditions for polynomial families of weighted backward shifts to share such vectors.

Proved non-existence results under certain conditions.

Abstract

We study common frequently hypercyclic vectors for countable families of weighted backward shifts acting on $\ell_p$ spaces, $1\leq p<\infty$. Using probabilistic techniques, we develop a general existence criterion, complemented by a non-existence result. These insights are then applied to the specific setting of countable families of polynomials of weighted backward shifts, providing conditions under which they share a common frequently hypercyclic vector.