6 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…