- 9h45-10h30 : Béatrice de Tilière (Université Paris Dauphine): Fock’s dimer model on the Aztec diamond
Abstract : We consider the dimer model, or equivalently domino tilings, on the Aztec diamond, and suppose that edges are assigned Fock’s weights. The main goal of this talk is to give a compact, explicit formula for the inverse Kasteleyn matrix, thus extending in this very general context previous results of the same kind; in particular, this gives an explicit expression for Boltzmann probabilities. Then, we will prove that the partition function admits a product form, and show how to recover Stanley’s celebrated formula as a specific case. Finally, we will show how our expression for the inverse Kasteleyn matrix allows to recover results about limit shapes. This is based on joint work with Cédric Boutillier.
Pause café de 10h30 à 11h
- 11h-11h45 : Ioannis Kontoyannis (University of Cambridge): Sumset bounds for the entropy on abelian groups.
Abstract: Information-theoretic ideas, tools and techniques have been influential in probability theory since at least the 1960s, and in the past 10-20 years Imre Rusza, Terry Tao and others have also developed deep connections between information-theoretic results and additive combinatorics. After briefly outlining some of the milestones of this historical development, we will describe some of our recent results on the interface between information theory, probability, additive combinatorics, and high-dimensional convex geometry.
- 11h45-12h30 : Jan Maas (IST Austria): Anisotropic transport-information inequalities.
Abstract: We prove upper bounds on the $L^\infty$-Wasserstein distance between strongly log-concave probability densities and log-Lipschitz perturbations. In the simplest setting, such a bound amounts to a transport-information inequality involving the $L^\infty$-Wasserstein metric and the relative $L^\infty$-Fisher information. We show that this inequality can be sharpened significantly in situations where the involved densities are anisotropic. Our proof is based on probabilistic techniques using Langevin dynamics. As an application of these results, we generalise a recent result by Calvez, Poyato, and Santambrogio on the rate of convergence in Fisher’s infinitesimal model from dimension 1 to arbitrary dimensions. This is joint work with Ksenia Khudiakova (ISTA) and Francesco Pedrotti (ISTA).
Repas du midi et café de 12h30 à 14h30
- 14h30 : soutenance de la thèse de Martin Rapaport intitulée "Courbure entropique sur les graphes et log-concavité discrète sur $Z^{d}$"
