Date: Tuesday, January 28, 2014
Title: Looperased random walk
Abstract: A number of models of random fractals arise as limits of discrete models with interactions. I will give a survey of one model, the looperased random walk (LERW), which arises from erasing loops of simple random walks. This process is also known as the Laplacian random walk in that the distribution of its growth is tied to the solution of the Dirichlet problem with value zero on the path.
The most interesting dimensions for this process are two and three. I will explain why and then discuss some of the behavior in these dimensions. I will emphasize two dimensions where the scaling limit is a ``conformally invariant'' random fractal with fractal dimension 5/4. The SchrammLoewner evolution (SLE) was developed to understand this process. If time allows, I will describe some recent work with M. Rezaei on the Minkowski content of the path and with C. BeneÅ¡ and F. Viklund on the convergence of the discrete Green's function of the looperased walk to the SLE Green's function.
This talk is intended for a general mathematical audience. It is not expected that the audience knows the terms in this abstract.
Speaker: Greg Lawler
Institution: University of Chicago
