Statistical Mechanics and Random Structures
Statistical mechanics describes the typical behavior of macroscopic systems based on knowledge of how their microscopic constituents interact. Many powerful methods and techniques have been developed in order to understand statistical mechanical systems. However, many of these lack a firm mathematical basis and providing a rigorous mathematical framework constitutes a major challenge to mathematicians.
Here we address questions that lie at the interface of probability theory, combinatorics, analysis, and both theoretical and mathematical physics and which contribute to providing a firm mathematical basis for well-established physics methods.
Primary research directions include:
- conformal invariance of lattice models
- random structures in higher dimensions
- conformal growth processes and extremal multi-fractals
- sharp asymptotics of correlations in models with finite correlation length
- asymptotic sphere packing density
- phase coexistence in random graphs
