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Çağrı Sert, Universität Zürich, Switzerland
March 2, 2022 @ 6:00 pm - 7:00 pm UTC+4
Title: “Stationary measures on projective spaces under block-Lyapunov domination”
Abstract: A probability measure on the general linear group of d*d-invertible matrices induces a non-commutative random walk on this group and a Markov chain on the projective space of R^d. The understanding of various asymptotic properties (in particular, its stationary measures) of this Markov chain is crucial for the study of the random walk on the general linear group. Whereas the pioneering works of Furstenberg, Kesten, Guivarc’h have given a satisfactory description when the measure is irreducible, many natural questions persist in the reducible case. In this work, under a block-domination condition for the top Lyapunov exponents, we give a description of stationary measures which refines works of Furstenberg–Kifer and Hennion from ’80s and also generalizes recent work by Aoun-Guivarc’h and Benoist-Bruère. After reviewing the well-known aspects of the theory, we will discuss our results, techniques and further consequences. Joint work with R. Aoun.