A probabilistic version of the Frequent Hypercyclicity Criterion
Studia Mathematica, Tome 176 (2006) no. 3, p. 279.

Voir la notice de l'article dans European Digital Mathematics Library

For a bounded operator T on a separable infinite-dimensional Banach space X, we give a "random" criterion not involving ergodic theory which implies that T is frequently hypercyclic: there exists a vector x such that for every non-empty open subset U of X, the set of integers n such that Tⁿx belongs to U, has positive lower density. This gives a connection between two different methods for obtaining the frequent hypercyclicity of operators.
Classification : 46B09, 47A16, 47A35
Mots-clés : linear dynamical systems, frequently hypercyclic operators, frequent hypercyclicity criterion, Gaussian mesures, Gaussian sums of Banach spaces 
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Sophie Grivaux. A probabilistic version of the Frequent Hypercyclicity Criterion. Studia Mathematica, Tome 176 (2006) no. 3, p. 279. https://geodesic-test.mathdoc.fr/item/STUMA_2006__176_3_284406/