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, UniversitÃ© de GenÃ¨ve.