Title: Limit Theorems and Random Fractal Curves in Statistical Mechanics

Abstract:
Rigorous statistical mechanics is an area of probability theory which deals with stochastic systems that have a large number of components and for which geometry often plays an important role. The main goal is to understand their average behavior and deviations from that. Statistical mechanics has many applications to physics and other fields, but in this talk I will focus on its mathematical theory. For concreteness, I will discuss two particular (two-dimensional) models, percolation and the Ising model, with a long history. After introducing the two models, I will present an approach to the study of two-dimensional systems that leads to a special family of random fractal curves and that has produced, in the last fifteen years, major breakthroughs and deep theorems.

Location: KdVI meeting room, SP 105-107, room F3.20.