A mathematical viewpoint on disorder relevance and on the infinite disorder renormalization group fixed point.
12th June 2020, 3:30 pm – 4:30 pm
In several statistical mechanics systems quenched disorder (random environment) ends up playing a dominant role over other sources of randomness (for example, thermal randomness). In reality what is behind these phenomena is often something that is rather familiar to probabilists, i.e. the effect of rare regions on global properties. The Renormalization Group (RG) approach to these systems was initiated by Ma and Dasgupta (end of 70s) and greatly developed by D. Fisher (in the 90s) who proposed in particular an explicit characterization of the RG fixed point when the disorder has a one dimensional structure. I will give a quick and partial overview of models to which these ideas have been applied and I will then focus on mathematical results. (A. s.) I will restrict myself to the case of the pinning models, that are just based on a renewal processes with heavy tails. The aim of the talk will be to present, as far as possible, old and recent results, along with some open problems and conjectures, on this class of models and in the light of the RG ideas.