13 citations · 55 across the 12 of their papers we have counts for
14 papers
On arithmetic functions orthogonal to deterministic sequences
Adam Kanigowski, Joanna Kulaga-Przymus, Mariusz Lemańczyk +1
We prove Veech's conjecture on the equivalence of Sarnak's conjecture on Möbius orthogonality with a Kolmogorov type property of Furstenberg systems of the M\''obius function. This…
M{ö}bius orthogonality in density for zero entropy dynamical systems
Alexander Gomilko, Mariusz Lemańczyk, Thierry de La Rue
It is proved that whenever a zero entropy dynamical system has only countably many ergodic measures and stands for the arithmetic M{ö}bius function, then there exists a…
Ergodic Poisson Splittings
Elise Janvresse, Emmanuel Roy, Thierry De La Rue
In this paper we study splittings of a Poisson point process which are equivariant under a conservative transformation. We show that, if the Cartesian powers of this transformation…
Automorphisms with quasi-discrete spectrum, multiplicative functions and average orthogonality along short intervals
El Houcein El Abdalaoui, Mariusz Lemanczyk, Thierry De La Rue
We show that Sarnak's conjecture on Möbius disjointness holds in every uniquely ergodic modelof a quasi-discrete spectrum automorphism. A consequence of this result is that, for ea…
Notes on Austin's multiple ergodic theorem
Thierry De la Rue
The purpose of this note is to present my understanding of Tim Austin's proof of the multiple ergodic theorem for commuting transformations, emphasizing on the use of joinings, ext…
Transposition game
Elise Janvresse, Steve Kalikow, Thierry De La Rue
We introduce a two-player game, in which each player extends a given sequence by picking a free element in a domain D of the real line. The aim of the players is to control the par…