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arXiv · 2409.04235

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

Kevin Agneessens·Karl-G. Grosse-Erdmann
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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 Erd\H{o}s and R\'enyi 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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Kevin Agneessens, Karl-G. Grosse-Erdmann. 2024-09-06. Rate of growth of random analytic functions, with an application to linear dynamics. https://arxiv.org/abs/2409.04235

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