On the role of disorder in localization transitions


Il giorno martedi' 6 novembre 2007 alle ore 11.00, nell'aula 2BC/30 della Torre Archimede, il prof. Giambattista Giacomin (Universite' Paris 7) terra' un seminario dal titolo "On the role of disorder in localization transitions".

A basic, but very challenging question in statistical mechanics is the effect of disorder on phase transitions. Suppose for example that in a homogeneous system a phase transition is observed at a certain "critical" value of a parameter: is this value changed when we modify the interaction by introducing inhomogeneous potentials chosen as a typical realization of a centered random field? Then one can ask also whether the behavior of the system close to criticality changes or not.
I will introduce and discuss a class of models in which these questions have recently found some answers. These models are probabilistically very easily introduced, they are in fact just based on elementary discrete Markov chains. Renewal theory arguments and estimates turn out to be the main mathematical tool in the analysis.

Rif. int. F. Caravenna