Cutoff for geodesic path on hyperbolic manifolds
Joffrey MATHIEN
I2M, Université d'Aix-Marseille
Date(s) : 25/02/2025 iCal
14h30 - 15h30
For an ergodic dynamical system, the cutoff describes an abrupt transition to equilibrium. Historically introduced in seminal work by Diaconis, Shahshahani and Aldous for card shuffling and other random walks on finite groups, there are now numerous examples of Markov chains and Markov processes where the cutoff has been established. Most of the current examples are on finite spaces.
In this talk, we study cutoff for a geodesic-path process on compact hyperbolic manifolds, and we develop a spectral strategy introduced by Lubetzky and Peres in 2016 for Ramanujan graphs and further developed in different geometric contexts. In particular, we extend results obtained by Golubev and Kamber on Brownian motion in 2019 to any dimension and still are able to obtain cutoff under weaker hypothesis.
Joint work with C. Bordenave
Emplacement
I2M Saint-Charles - Salle de séminaire
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