A class of generalized Ornstein transformations with the weak mixing property
A class of nonstationary adic transformations
A note on ergodic transformations of self-similar Volterra Gaussian processes.
A note on mixing properties of invertible extensions.
A quantified Tauberian theorem for sequences
The main result of this paper is a quantified version of Ingham's Tauberian theorem for bounded vector-valued sequences rather than functions. It gives an estimate on the rate of decay of such a sequence in terms of the behaviour of a certain boundary function, with the quality of the estimate depending on the degree of smoothness this boundary function is assumed to possess. The result is then used to give a new proof of the quantified Katznelson-Tzafriri theorem recently obtained by the author...
About projections of logarithmic Sobolev inequalities
About the existence of the thermodynamic limit for some deterministic sequences of the unit circle.
About the existence of the thermodynamic limit for some deterministic sequences of the unit circle.
Almost sure limit theorems for dependent random variables
For a sequence of dependent random variables we consider a large class of summability methods defined by R. Jajte in [jaj] as follows: For a pair of real-valued nonnegative functions g,h: ℝ⁺ → ℝ⁺ we define a sequence of “weighted averages” , where g and h satisfy some mild conditions. We investigate the almost sure behavior of such transformations. We also take a close look at the connection between the method of summation (that is the pair of functions (g,h)) and the coefficients that measure...
Almost sure rates of mixing for i.i.d. unimodal maps
An extension which is relatively twofold mixing but not threefold mixing
We give an example of a dynamical system which is mixing relative to one of its factors, but for which relative mixing of order three does not hold.
Attracteurs, orbites et ergodicité
Bergelson's theorem for weakly mixing C*-dynamical systems
We study a nonconventional ergodic average for asymptotically abelian weakly mixing C*-dynamical systems, related to a second iteration of Khinchin's recurrence theorem obtained by Bergelson in the measure-theoretic case. A noncommutative recurrence theorem for such systems is obtained as a corollary.
Completely mixing maps without limit measure
We combine some results from the literature to give examples of completely mixing interval maps without limit measure.
Construction de cocycles en escalier ergodiques et faiblement mélangeants au-dessus de rotations irrationnelles du cercle
Convergence and uniqueness problems for Dirichlet forms on fractals
è un particolare operatore di minimizzazione per forme di Dirichlet definite su un sottoinsieme finito di un frattale che è, in un certo senso, una sorta di frontiera di . Viene talvolta chiamato mappa di rinormalizzazione ed è stato usato per definire su un analogo del funzionale e un moto Browniano. In questo lavoro si provano alcuni risultati sull'unicità dell'autoforma (rispetto a ), e sulla convergenza dell'iterata di rinormalizzata. Questi risultati sono collegati con l'unicità...
Convergence of iterates of a transfer operator, application to dynamical systems and to Markov chains
We present a spectral theory for a class of operators satisfying a weak “Doeblin–Fortet” condition and apply it to a class of transition operators. This gives the convergence of the series , , under some regularity assumptions and implies the central limit theorem with a rate in for the corresponding Markov chain. An application to a non uniformly hyperbolic transformation on the interval is also given.
Convergence of iterates of a transfer operator, application to dynamical systems and to Markov chains
We present a spectral theory for a class of operators satisfying a weak “Doeblin–Fortet" condition and apply it to a class of transition operators. This gives the convergence of the series ∑k≥0krPkƒ, , under some regularity assumptions and implies the central limit theorem with a rate in for the corresponding Markov chain. An application to a non uniformly hyperbolic transformation on the interval is also given.
Corrigendum : “Almost sure rates of mixing for i.i.d. unimodal maps”
Corrigendum to: Stable ergodicity and julienne quasi-conformality, J. Eur. Math. Soc. 2, 1-52