Rate of Growth of Frequently Hypercyclic Random Functions for Weighted Shifts

The search for admissible rates of growth for frequently hypercyclic functions with a probabilistic approach was initiated in a recent work by Nikula for the differentiation operator, and continued by Mouze and Munnier for the Taylor shift. We extend their approach by giving a criterion for general random series, and apply it to various frequently hypercyclic weighted shifts on the space of entire functions and on the space of holomorphic functions on the unit disk.