Stochastic Analysis, Stochastic Partial Differential Equations and Applications to Fluid Dynamics and Particle Systems

course: Some topics in Glauber dynamics for spin systems

speaker: Fabio Martinelli (Università di Roma Tre)

abstract: i) I first plan to introduce Glauber dynamics for the Ising model on a general bounded degree graph G. When G is the hypercubic lattice Z^d I will show that for d>1 the existence of multiple Gibbs measures at low temperature is reflected in a dramatic slowing down of the dynamics. Along the way I will review some of the most common methods (comparison arguments, paths argumenst and coupling) to bound the mixing time of reversible, continuous time Markov chains; ii) I will then illustrate the problem of analyzing the Glauber dynamics inside one specific phase for G the hypercubic lattice or a regular rooted tree; iv) I will finally discuss the connection between spin models on trees and recontruction problems on noisy channels.

timetable:
Wed 12 Jul, 10:30 - 12:30, Sala Conferenze Centro De Giorgi
Thu 13 Jul, 14:30 - 16:30, Sala Conferenze Centro De Giorgi
Fri 14 Jul, 10:30 - 12:30, Sala Conferenze Centro De Giorgi
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