Rate of growth of random analytic functions, with an application to linear dynamics

2024/09/06 by Kevin Agneessens, Agneessens, Kevin, Karl‐G. Grosse‐Erdmann +1
Mathematics · #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2409.04235

Abstract

We obtain Wiman-Valiron type inequalities for random entire functions and for random analytic functions on the unit disk that improve a classical result of Erdős and Rényi and recent results of Kuryliak and Skaskiv. Our results are then applied to linear dynamics: we obtain rates of growth, outside some exceptional set, for analytic functions that are frequently hypercyclic for an arbitrary chaotic weighted backward shift.

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