Cagri Sert - Stationary probability measures on projective spaces
| Dates: | 9 October 2024 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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Cagri Sert (University of Warwick) will speak at the Probability seminar.
Title: Stationary probability measures on projective spaces
Abstract:
We give a description of stationary probability measures for the Markov chains on projective spaces induced by iid random walks on $\GL_d(\R)$. This generalizes the work of Bougerol--Picard ('92) on affine stochastic recursion. As in that case, the analysis is carried out in three parts: the contracting, expanding, and the more subtle critical case. In the first part, I will focus on the contracting case, which also yields a new interesting class of stationary probability measures and fractals on projective spaces. In the second part, I will mention the results in the critical case and make connection with the works of Furstenberg--Kifer, Guivarc'h--Raugi and Benoist--Quint. Combination of all these works allows to get a complete description of stationary probability measures. Joint works with Richard Aoun.
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