We provide with criteria for a family of sequences operators to share frequently universal vector. These are inspired by the classical Frequent Hypercyclicity Criterion and recent criterion due Grivaux, Matheron Menet where periodic points play central role. As an application, we obtain any operator T in specific class acting on separable Banach space, necessary sufficient condition subset ? co...

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