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Cagri Sert - Stationary probability measures on projective spaces

Dates:9 October 2024
Times:15:00 - 16:00
What is it:Seminar
Organiser:Department of Mathematics
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  • In category "Seminar"
  • In group "(Maths) Probability and statistics"
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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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Jose Pedraza Ramirez

jose.pedrazaramirez@manchester.ac.uk

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