Title: Random curves, scaling limits and Loewner evolutions

Abstract:
In the 2D statistical physics and its lattice models, interfaces are  
random curves. A general strategy to prove the convergence of a random  
discrete curve, as the lattice mesh goes to zero, is first to  
establish precompactness of the law giving the existence of  
subsequential scaling limits and then to prove the uniqueness. In this  
talk, I will introduce a sufficient condition that guarantees the  
precompactness and also that the limits are Loewner evolutions, i.e.  
they correspond to continuous Loewner driving processes. This  
framework of estimates is applicable in almost all proofs aiming to  
establish that an interface converges to a Schramm-Loewner evolution  
(SLE). In principle, it can be applied beyond SLE.

Joint work with Stanislav Smirnov, Université de Genève.