60 citations · 98 across the 21 of their papers we have counts for
22 papers
Frequencies of Patterns in Smooth Sequences Over the Alphabet
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 of…
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…
Furstenberg systems of pretentious and MRT multiplicative functions
Nikos Frantzikinakis, Mariusz Lemańczyk, Thierry de la Rue
We prove structural results for measure preserving systems, called Furstenberg systems, naturally associated with bounded multiplicative functions. We show that for all pretentious…
A central limit theorem for the variation of the sum of digits
Yohan Hosten, Élise Janvresse, Thierry de la Rue
We prove a Central Limit Theorem for probability measures defined via the variation of the sum-of-digits function, in base . For and , we conside…
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…
Poisson suspensions and Sushis
Elise Janvresse, Emmanuel Roy, Thierry De La Rue
In this paper, we prove that ergodic point processes with moments of all orders, driven by particular infinite measure preserving transformations, have to be a superposition of shi…
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…
Standardness of monotonic Markov filtrations
Elise Janvresse, Stéphane Laurent, Thierry De La Rue
We derive a practical standardness criterion for the filtration generated by a monotonic Markov process. This criterion is applied to show standardness of some adic filtrations.
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…
Around King's Rank-One theorems: Flows and Z^n-actions
Élise Janvresse, Thierry De La Rue, Valery Ryzhikov
We study the generalizations of Jonathan King's rank-one theorems (Weak-Closure Theorem and rigidity of factors) to the case of rank-one R-actions (flows) and rank-one Z^n-actions.…
Averaging along Uniform Random Integers
Élise Janvresse, Thierry De La Rue
Motivated by giving a meaning to "The probability that a random integer has initial digit d", we define a URI-set as a random set E of natural integers such that each n>0 belongs t…
Zero Krengel Entropy does not kill Poisson Entropy
Élise Janvresse, Thierry De La Rue
We prove that the notions of Krengel entropy and Poisson entropy for infinite-measure-preserving transformations do not always coincide: We construct a conservative infinite-measur…
Almost-sure Growth Rate of Generalized Random Fibonacci sequences
Elise Janvresse, Benoît Rittaud, Thierry De La Rue
We study the generalized random Fibonacci sequences defined by their first nonnegative terms and for , (linear case) and $\widetilde F_{n+2}…
Pinning by a sparse potential
Élise Janvresse, Thierry De La Rue, Yvan Velenik
We consider a directed polymer interacting with a diluted pinning potential restricted to a line. We characterize explicitely the set of disorder configurations that give rise to l…