Speaker
Antti Kemppiainen
(University of Helsinki)
Description
Random curves arise naturally as interfaces in the 2D
statistical physics and its lattice models. 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
Joint work with Stanislav Smirnov, Université de Genève
