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Home » RAS - Research Seminar (Part 1): Recurrence on affine grassmannians

Seminar

RAS - Research Seminar (Part 1): Recurrence on affine grassmannians November 02, 2020 (09:00 AM PST - 10:00 AM PST)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) Yves Benoist (Centre National de la Recherche Scientifique (CNRS))
Description

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

This is one of the research seminars for the RAS program, that distinguishes itself from the postdocs and program associates seminars in that speakers are chosen among Research Members, Research Professors with occasional outside speakers.

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To participate in this seminar, please register here: https://www.msri.org/seminars/25205

Abstract:

We study the action of the affine group G on the space X of k-dimensional affine subspaces of the d-dimensional affine space. More precisely, given a compactly-supported Zariski dense probability measure on G, we want to know when the associated random walk on X is positively recurrent or, equivalently, when does X supports a stationary probability measure. We show, with C. Bruere, that this is the case if and only if at most k Lyapunov exponents are non negative. In particular, when the probability measure is symmetric, positive recurrence happens if and only if the dimension k is at least half the dimension d.

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