Il prof. Fabio Toninelli (Univ. Lyon 1, France) terra' un corso di dottorato di 12 ore circa presso il dipartimento di Matematica e Fisica di Roma Tre.

Title: Dimer models: thermodynamics, fluctuations and Glauber dynamics

Dates: March 9, 11, 16, 18, 23, 25, 30 and April 1st, 2015

Time:11.00-12.45

Location: Room 311 (third floor, palazzina C) Dipartimento di Matematica e Fisica, Roma Tre, L.go Murialdo 1 - 00146 Roma

Course description:

We will discuss several aspects of the mathematical theory of models of lattice dimers. These classical, two- dimensional statistical mechanics models are in certain sense “exactly solvable” (Kasteleyn, 1961). Recently there is a revival of interest in dimer models among probabilists and mathematical physiciscs, due to their properties of conformal invariance and of “Gaussian Free Field”-type fluctuations. Another aspect of great interest (in probability and theoretical computer science) is the study of the associated Markov dynamics (Glauber dynamics). In particular, a natural question concerns the speed of convergence of the dynamics to its invariant measure.

Contents:

– Kasteleyn theory (computation of the partition function)

– dimer-dimer correlations, determinantal representation

– dimer models as “lattice free fermions”

– height function and its convergence to the “Gaussian Free Field”

– thermodynamic limit: translation-invariant Gibbs states and limit shape

– Glauber dynamics for dimer models. Connection with the zero-temperature

– The problem of the speed of convergence