CIRM - Videos & books Library

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

Concentration is an important property of independent random variable, showing that any reasonable function of such variables does not vary a lot around its mean. Observables generated by the iteration of a chaotic enough dynamical system often share a lot of properties with independent random variables. In this survey talk, we discuss several situations where one can prove concentration for them, in uniformly or non-uniformly hyperbolic situations. We also explain why such a property is important to answer relevant geometric or dynamical questions.
concentration - martingales - dynamical systems - Young towers - uniform hyperbolicity - moment bounds[-]

Concentration is an important property of independent random variable, showing that any reasonable function of such variables does not vary a lot around its mean. Observables generated by the iteration of a chaotic enough dynamical system often share a lot of properties with independent random variables. In this survey talk, we discuss several situations where one can prove concentration for them, in uniformly or non-uniformly hyperbolic ...[+]

37A25 ; 37A50 ; 60F15

Sélection Signaler une erreur

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

37A25 ; 37A50 ; 60F17 ; 60G10

Sélection Signaler une erreur

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

For any countable group, and also for any locally compact second countable, compactly generated topological group, $G$, there exists a "universal" hypercyclic representation on a Hilbert space, in the sense that it simultaneously models every possible ergodic probability measure preserving free action of $G$. I will discuss the original proof of this theorem (a joint work with Benjy Weiss) and then, at the end of the talk, say some words about the development of this idea and its applications as expounded in a subsequent work of Sophie Grivaux.[-]

For any countable group, and also for any locally compact second countable, compactly generated topological group, $G$, there exists a "universal" hypercyclic representation on a Hilbert space, in the sense that it simultaneously models every possible ergodic probability measure preserving free action of $G$. I will discuss the original proof of this theorem (a joint work with Benjy Weiss) and then, at the end of the talk, say some words about ...[+]

37A15 ; 37A05 ; 37A25 ; 37A30 ; 47A16 ; 47A67 ; 47D03

Sélection Signaler une erreur

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

We will consider (sub)shifts with complexity such that the difference from $n$ to $n+1$ is constant for all large $n$. The shifts that arise naturally from interval exchange transformations belong to this class. An interval exchange transformation on d intervals has at most $d/2$ ergodic probability measures. We look to establish the correct bound for shifts with constant complexity growth. To this end, we give our current bound and discuss further improvements when more assumptions are allowed. This is ongoing work with Michael Damron.[-]

We will consider (sub)shifts with complexity such that the difference from $n$ to $n+1$ is constant for all large $n$. The shifts that arise naturally from interval exchange transformations belong to this class. An interval exchange transformation on d intervals has at most $d/2$ ergodic probability measures. We look to establish the correct bound for shifts with constant complexity growth. To this end, we give our current bound and discuss ...[+]

37B10 ; 37A25 ; 68R15

Sélection Signaler une erreur

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

The classic mean ergodic theorem has been extended in numerous ways: multiple averages, polynomial iterates, weighted averages, along with combinations of these extensions. I will give an overview of these advances and the different techniques that have been used, focusing on convergence results and what can be said about the limits.

37A05 ; 37A25 ; 37A15

Sélection Signaler une erreur

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

The classic mean ergodic theorem has been extended in numerous ways: multiple averages, polynomial iterates, weighted averages, along with combinations of these extensions. I will give an overview of these advances and the different techniques that have been used, focusing on convergence results and what can be said about the limits.

37A05 ; 37A25 ; 37A15

Sélection Signaler une erreur

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

The classic mean ergodic theorem has been extended in numerous ways: multiple averages, polynomial iterates, weighted averages, along with combinations of these extensions. I will give an overview of these advances and the different techniques that have been used, focusing on convergence results and what can be said about the limits.

37A05 ; 37A25 ; 37A15

Sélection Signaler une erreur

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

The behaviour of infinite translation surfaces is, in many regards, very different from the finite case. For example, the geodesic flow is often not recurrent or is not even defined for infinite time in a generic direction.
However, we show that if one focuses on a class of infinite translation surfaces that exclude the obvious counter-examples, one can adapted the proof of Kerckhoff, Masur, and Smillie and show that the geodesic flow is uniquely ergodic in almost every direction. We call this class of surface essentially finite.
(joint work with Anja Randecker).[-]

The behaviour of infinite translation surfaces is, in many regards, very different from the finite case. For example, the geodesic flow is often not recurrent or is not even defined for infinite time in a generic direction.
However, we show that if one focuses on a class of infinite translation surfaces that exclude the obvious counter-examples, one can adapted the proof of Kerckhoff, Masur, and Smillie and show that the geodesic flow is ...[+]

37D40 ; 51A40 ; 37A25

Sélection Signaler une erreur

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

We obtain results on mixing and rates of mixing for infinite measure semiflows and flows. The results on rates of mixing rely on operator renewal theory and a Dolgopyat-type estimate. The results on mixing hold more generally and are based on a deterministic (ie non iid) version of Erickson's continuous time strong renewal theorem.

37A25 ; 37A40 ; 37A50 ; 37D25

Sélection Signaler une erreur

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

I will consider the asymmetric simple exclusion process on a linear lattice of N sites, and I will present a result on the asymptotic (in N) behaviour of the distance to equilibrium of this process starting from the "worst" initial condition. This result shows a cutoff phenomenon: instead of decaying smoothly with time, the distance to equilibrium falls abruptly at some deterministic time. This is a joint work with Hubert Lacoin (IMPA).

60J27 ; 37A25 ; 82C22

Sélection Signaler une erreur

TUTELLES

PARTENAIRES

Destination de la recherche

Raccourcis

Documents 37A25 17 résultats

Concentration properties of dynamical systems - Gouëzel, Sébastien (Auteur de la conférence) | CIRM Nouveau

The almost sure invariance principle for beta-mixing measures - Haydn, Nicolai (Auteur de la conférence) | CIRM Nouveau

A universal hypercyclic representation - Glasner, Eli (Auteur de la conférence) | CIRM H Nouveau

Ergodic measures for subshifts with eventually constant growth - Fickenscher, Jon (Auteur de la conférence) | CIRM H Nouveau

Multiple ergodic theorems: old and new - Lecture 1 - Kra, Bryna (Auteur de la conférence) | CIRM H Nouveau

Multiple ergodic theorems: old and new - Lecture 2 - Kra, Bryna (Auteur de la conférence) | CIRM H Nouveau

Multiple ergodic theorems: old and new - Lecture 3 - Kra, Bryna (Auteur de la conférence) | CIRM H Nouveau

Unique ergodicity of geodesic flow in an infinite translation surface - Rafi, Kasra (Auteur de la conférence) | CIRM H Nouveau

Mixing and rates of mixing for infinite measure flows - Melbourne, Ian (Auteur de la conférence) | CIRM H Nouveau

Cutoff phenomenon for the asymmetric simple exclusion process - Labbé, Cyril (Auteur de la conférence) | CIRM H Nouveau