Dear colleagues,

I would like to announce the following online seminar organized by the Probability group of the University of Pisa. The talks will be accessible under the link

Click here to join the meetinghttps://teams.microsoft.com/l/meetup-join/19%3a17115d7f6ef44c5e91974362906cfc95%40thread.tacv2/1604838519533?context=%7b%22Tid%22%3a%22c7456b31-a220-47f5-be52-473828670aa1%22%2c%22Oid%22%3a%22dfd1e5f6-331d-43e0-a180-4bb6ce727fb7%22%7d

Best regards,

Giacomo

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Tuesday, Nov. 10, 14:00

Speaker: Giovanni Conforti (École Polytechnique)

Title: A probabilistic approach to convex entropy decay for Markov chain

Abstract: A powerful technique to quantify the trend to equilibrium and the best constants in the associated functional inequalities for diffusions on Riemannian manifolds consists in establishing convexity estimates for the relative entropy via the so called Gamma calculus. In order to adapt these ideas to the context of discrete Markov chains several notions of discrete curvature have been recently introduced and used to obtain concrete lower bounds for the logarithmic Sobolev constant in a number of situations. However, the picture is not fully clear yet and several natural questions remain unanswered. In this talk, I will present a more probabilistic approach to convex entropy decay which relies on the notion of coupling rates to bypass or replace discrete Böchner identities. If time allows, I will show how this approach produces explicit lower bounds in non perturbative setting, thus going beyond the weak-interaction/low high temperature regime.

Tuesday, Nov. 10, 15:00

Speaker: Ruojun Huang (Scuola Normale Superiore)

Title: Averaging principle and random growth

Abstract: Motivated by questions in reinforced random walks and the asymptotic shape of their range, we study a simplified model of random growth in the continuum. In this model, random sets grow by increment of small bumps at the boundary, driven by a particle that is confined to move in its interior, reinforced by the last location of domain's increment. We prove scaling limit of the growing domain to an infinite dimensional ODE, when the bump size is sent to zero. We deduce a macroscopic shape theorem for the growing domain with fixed bump size, as time tends to infinity. Joint work with Amir Dembo, Pablo Groisman, and Vladas Sidoravicius.