Pacific Institute for the Mathematical Sciences - PIMS

Using multiple SLE to explain a certain observable in the 2d Ising model

The Schramm-Loewner evolution (SLE) is a one-parameter family of random
growth processes that has been successfully used to analyze a number of
models from two-dimensional statistical mechanics. Currently there is
interest in trying to formalize our understanding of conformal field
theory using SLE. Smirnov recently showed that the scaling limit of
interfaces of the 2d critical Ising model can be described by SLE(3).
The primary goal of this talk is to explain how a certain non-local
observable of the 2d critical Ising model studied by Arguin and
Saint-Aubin can be rigorously described using multiple SLE(3) and
Smirnov's result. As an extension of this result, we explain how to
compute the probability that a Brownian excursion and an SLE(k) curve,
0<4, do not intersect.

3:00pm-4:00pm, WMAX 216