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