Limit shapes and integrability

Nicolai Reshetikhin

Berkeley

Mon, Mar. 21st 2016, 11:00-12:00

Salle Claude Itzykson, Bât. 774, Orme des Merisiers

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 variablecan 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. \par 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.

Contact : Vincent
PASQUIER