Bassam Fayad

Institut de Mathématiques de Jussieu-Paris Rive Gauche

Multilple Borel Cantelli lemma and applications

Ergodic Theory and Dynamical Systems Seminar

26th November 2020, 2:00 pm – 3:00 pm
Online via Zoom, Link to be released to the seminar email list a few days before the seminar

The Borel Cantelli lemma is a classical tool to decide whether almost surely an infinite number of rare events are realized.
It does not give however any information on the repartition in time of the realizations. We extend the Borel Cantelli lemma to characterize the realization (infinitely many times) of multiple events in a same time scale.

Dynamical versions of this extension allow to characterize multiple recurrence and multiple hitting of shrinking targets for exponentially dynamical mixing systems. Among the applications are multilog laws for geodesic excursions (generalizing Sullivan's logarithm law) as well as for Diophantine approximations (generalizing the Khintchine-Groshev theorems).
This is a joint work with Dmitry Dolgopyat et Sixu Liu.

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