Friday, April 13, 2012

The Schramm-Loewner Evolution

Christian Benes
(Department of Mathematics, Brooklyn College / CUNY, USA)

Abstract: The Schramm-Loewner evolution (SLE) is a one-parameter family of conformally invariant stochastic growth processes in the complex plane introduced by O. Schramm in 1999 which is known to describe the continuum limit of a variety of statistical mechanics models. For example, the loop-erased random walk converges to SLE(2), the interface of the Ising model at criticality converges to SLE(3), and the percolation exploration process on the hexagonal lattice converges to SLE(6). It is also known that if the scaling limit of self-avoiding walk exists and is conformally invariant, then it must be SLE(8/3). The goal of this talk is to give a gentle introduction to SLE and, if time permits, discuss recent progress in deriving rates of convergence of loop-erased random walk to SLE(2).

Friday, April 13, 2012
Time: 11h00
Room: Sala IAPMEI, Edificio Quelhas, ISEG