Convergence d'une suite le long de sous-suites d'indices à croissance exponentielle
Existence et unicité d’une probabilité invariante pour des translations aléatoires de
Résolution d'une équation fonctionnelle
Théorèmes ergodiques ponctuels pour des mesures diagonales. Cas des systèmes distaux
On the sequence of integer parts of a good sequence for the ergodic theorem
If is a sequence of real numbers which is good for the ergodic theorem, is the sequence of the integer parts good for the ergodic theorem ? The answer is negative for the mean ergodic theorem and affirmative for the pointwise ergodic theorem.
Propriétés ergodiques des suites -multiplicatives
Large deviations for generic stationary processes
Let (Ω,A,μ,T) be a measure preserving dynamical system. The speed of convergence in probability in the ergodic theorem for a generic function on Ω is arbitrarily slow.
Van der Corput sets in
In this partly expository paper we study van der Corput sets in , with a focus on connections with harmonic analysis and recurrence properties of measure preserving dynamical systems. We prove multidimensional versions of some classical results obtained for d = 1 by Kamae and M. Mendès France and by Ruzsa, establish new characterizations, introduce and discuss some modifications of van der Corput sets which correspond to various notions of recurrence, provide numerous examples and formulate some...
Sur un théorème ergodique pour des mesures diagonales
Théorèmes ergodiques pour des mesures diagonales
Generic points in the cartesian powers of the Morse dynamical system
The symbolic dynamical system associated with the Morse sequence is strictly ergodic. We describe some topological and metrical properties of the Cartesian powers of this system, and some of its other self-joinings. Among other things, we show that non generic points appear in the fourth power of the system, but not in lower powers. We exhibit various examples and counterexamples related to the property of weak disjointness of measure preserving dynamical systems.
Un théorème ergodique polynômial ponctuel pour les endomorphismes exacts et les K-systèmes
Sets of -recurrence but not -recurrence
For every , we produce a set of integers which is -recurrent but not -recurrent. This extends a result of Furstenberg who produced a -recurrent set which is not -recurrent. We discuss a similar result for convergence of multiple ergodic averages. We also point out a combinatorial consequence related to Szemerédi’s theorem.
Étude asymptotique d'une marche aléatoire centrifuge
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