Limit shapes for the 6-vertex model in statistical mechanics (Nicolai Reshetikhin, UC Berkeley & U Amsterdam)

10.03.2016 16:15

The phenomenon of limit shape formations in statistical mechanics is similar in many ways to the semiclassical limit in quantum mechanics. Its main feature is that for large systems random variable can become deterministic at certain scales. Versions of this phenomenon are known as hydrodynamical limits. In probability theory counterparts of limit shape formation are central limit theorems. The phenomenon was relatively well studied in dimer models where the corresponding variational principle is proven. The first part of this talk will be an overview of the variational principle for the limit shape formation in dimer models. In the second part I will show that under certain assumptions, non-linear PDE describing limit shapes in the 6-vertex model have infinitely many conserved quantities.

Lieu

Room 17, Colloque

entrée libre