60 citations · 98 across the 21 of their papers we have counts for
12 papers · 1 filter
Frequency of patterns in smooth sequences over the alphabet \{1, 3\}
Damien Jamet, Irène Marcovici, Léo Poirier +1
We provide an ergodic theory framework to study statistical properties of smooth sequences over the odd alphabet {1, 3}. The arithmetic nature of this alphabet yields a partition o…
On orthogonality to uniquely ergodic systems
Martyna Górska, Mariusz Lemańczyk, Thierry de la Rue
We solve Boshernitzan's problem of characterization (in terms of so called Furstenberg systems) of bounded sequences that are orthogonal to all uniquely ergodic systems. Some varia…
A note on Sarnak processes
Mariusz Lemańczyk, Michal D. Lemańczyk, Thierry de La Rue
Basic properties of stationary processes called Sarnak processes are studied. As an application, a combinatorial reformulation of Sarnak's conjecture on M{ö}bius orthogonality is p…
Confined Poisson extensions
Séverin Benzoni, Emmanuel Roy, Thierry de la Rue
This paper follows on from our previous work, where we introduced the notion of \emph{confined extensions}, and our purpose is to widen the context in which such extensions appear.…
Joining properties of automorphisms disjoint with all ergodic systems
Przemysław Berk, Martyna Górska, Thierry de la Rue
We study the class of automorphisms which are disjoint with all ergodic systems. We prove that the identities are the only multipliers of that is, each aut…
On Furstenberg systems of aperiodic multiplicative functions of Matomaki, Radziwill and Tao
Aleksander Gomilko, Mariusz Lemanczyk, Thierry de la Rue
It is shown that in a class of counterexamples to Elliott's conjecture by Matomaki, Radziwill and Tao, the Chowla conjecture holds along a subsequence.
Möbius disjointness for models of an ergodic system and beyond
El Houcein El Abdalaoui, Joanna Kułaga-Przymus, Mariusz Lemańczyk +1
Given a topological dynamical system and an arithmetic function , we study the strong MOMO property (relatively to $\boldsymbol…
Invariant measures for Cartesian powers of Chacon infinite transformation
Elise Janvresse, Emmanuel Roy, Thierry De La Rue
We describe all boundedly finite measures which are invariant by Cartesian powers of an infinite measure preserving version of Chacon transformation. All such ergodic measures are…
The Chowla and the Sarnak conjectures from ergodic theory point of view
El Houcein El Abdalaoui, Joanna Kulaga-Przymus, Mariusz Lemanczyk +1
We rephrase the conditions from the Chowla and the Sarnak conjectures in abstract setting, that is, for sequences of numbers in {-1,0,1}, and introduce several natural generalizati…
A dynamical point of view on the set of B-free integers
El Houcein El Abdalaoui, Mariusz Lemanczyk, Thierry De La Rue
We extend the study of the square-free flow, recently introduced by Sarnak, to the more general context of B-free integers, that is to say integers with no factor in a given family…
Weak limits of powers of Chacon's automorphism
Élise Janvresse, A. A. Prikhod'Ko, Thierry De La Rue +1
We completely describe the weak closure of the powers of the Koopman operator associated to Chacon's classical automorphism. We show that weak limits of these powers are the ortho-…
On spectral disjointness of powers for rank-one transformations and Möbius orthogonality
El Houcein El Abdalaoui, Mariusz Lemanczyk, Thierry De La Rue
We study the spectral disjointness of the powers of a rank-one transformation. For a large class of rank-one constructions, including those for which the cutting and stacking param…