Séminaire Probabilités et Statistiques
Discrete curvatures and the cutoff phenomenon
13
Feb. 2025
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13
Feb. 2025
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Intervenant : Francesco Pedrotti
Institution : Ceremade, PSL
Heure : 14h00 - 15h00
Lieu : 3L15

Ricci curvature plays a fundamental role in the analysis of diffusion processes on Riemannian manifolds. In particular, positive lower bounds lead to important consequences in terms of functional inequalities, concentration of measure, and speed of convergence to equilibrium. This motivates the search for suitable notions of positive curvature in more general settings, such as Markov chains in discrete spaces. Several definitions have been proposed by adapting equivalent characterizations of Ricci curvature, but unlike in the smooth setting, these turn out to be non-equivalent, each with its own advantages and limitations. In this talk (based on joint work with Justin Salez), I will review some notions of curvature in this context and discuss some recent developments, with applications to the cutoff phenomenon.

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