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An Isaac Newton Institute Workshop

Non-Equilibrium Dynamics of Interacting Particle Systems

Stochastic Loewner Evolution and other growth processes in two dimensions

30th March 2006

Author: Cardy, JL (University of Oxford)

Abstract

Random objects such as clusters in the plane can often be described in terms of the conformal mappings which take their boundaries into some standard shape. As the clusters grow, the mapping function changes in a well-defined manner, which is often easier to understand than the original problem. One of the simplest examples is Stochastic Loewner Evolution (SLE), which turns out to describe random curves in equilibrium statistical mechanics models. These lectures will give an introduction to the use of such conformal mappings, and to SLE in particular, from the physicist's point of view.