Groupe de travail "théorie ergodique"

Groupe de travail de théorie ergodique

Coorganisé avec Matthieu Joseph. Le groupe de travail se réunit tous les vendredis à 10h en salle 1013 du bâtiment Sophie Germain.

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vendredi 9 janvier, 10:00

BBB

Some (more) ergodic properties of Poisson boundaries and applications

Poisson boundaries represent the asymptotic significant behaviour of a stochastic process on a group. I will present some of their strong ergodic properties, and show that they naturally appear in some superrigidity problems in higher rank. This will be a sort of continuation of Antoine Derimay's talks, but I will introduce all the concepts.

Prévisions : second exposé de Corentin le 23 janvier (à confirmer).

Séances précédentes

3 octobre : Random walks and Poisson boundaries in ergodic theory I (Antoine Derimay). Voici l'enregistrement et les notes. Abstract

To a random walk on a group, one can associate a measured space on which the group acts by measure-class preserving automorphisms, called the Poisson boundary of the walk. This action is the equality case of entropy inequalities, and it satisfies strong ergodic properties and is amenable, which makes it a boundary in the sense of Bader-Furman. As such, a good understanding of this action can lead to various interesting rigidity results.

10 octobre : Random walks and Poisson boundaries in ergodic theory II (Antoine Derimay). Voici l'enregistrement et les notes.

14 novembre : The Poisson point process from scratch I (Sam Mellick) Voici l'enregistrement et des notes détaillées. Abstract

The Poisson point process is a fundamental object from stochastic geometry, with many real world applications. I will present this object from the ergodic theoretic perspective, and show in full detail how it is constructed, as well as prove many of its basic properties. Some probability theory knowledge will be assumed (but only a first undergrad probability course, and I will remind everyone of the key tools needed as they come up).

Whilst there is no particular guiding goal theorem, one should note that the Poisson point process has played an integral role in recent breakthroughs for proving fixed price one for higher rank semisimple Lie groups and products of groups, and this hopefully serves as sufficient motivation.

5 décembre : The Poisson point process from scratch II (Sam Mellick) Voici l'enregistrement et des notes détaillées.