On the rate of growth of random analytic functions, with an application to linear dynamics

frequently hypercyclic entire function; Lévy's phenomenon; rate of growth; subgaussian random variable; Wiman-Valiron inequality; Wiman-Valiron theory; Mathematics (all)

Abstract :

[en] 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 Erdõs andRényi 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.

Disciplines :

Mathematics

Author, co-author :

Agneessens, Kevin ; Université de Mons - UMONS > Faculté des Sciences > Service d'Analyse fonctionnelle

Grosse-Erdmann, Karl-G. ; Université de Mons, Département de Mathématique, Mons, Belgium

Language :

English

Title :

On the rate of growth of random analytic functions, with an application to linear dynamics

Publication date :

2025

Journal title :

Canadian Journal of Mathematics

ISSN :

0008-414X

eISSN :

1496-4279

Publisher :

Cambridge University Press

Pages :

1-21

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0008414X25101491

Research unit :

S844 - Analyse fonctionnelle

Research institute :

Complexys

Available on ORBi UMONS :

since 29 May 2026

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Bibliography

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