Federico Camia

Title: Limit Laws and Statistical Mechanics

Abstract: Statistical mechanics deals with stochastic systems that have a large number of components. For this reason, probability theory plays an essential role in the mathematical analysis of the subject. After a gentle introduction to the subject, I will give a nontechnical overview of recent, exciting developments that combine in a beautiful and unexpected way discrete probability, stochastic processes and complex analysis. For concreteness, I will discuss two specific models, percolation and the Ising model, which have a long history, played an important role in the development of statistical mechanics, and occupy a central place in modern probability theory.