The Loewner equation: maps and shapes
Statistical Mechanics
2007-05-23 v1
Abstract
In the last few years, new insights have permitted unexpected progress in the study of fractal shapes in two dimensions. A new approach, called Schramm-Loewner evolution, or SLE, has arisen through analytic function theory and probability theory, and given a new way of calculating fractal shapes in critical phenomena, the theory of random walks, and of percolation. We present a non-technical discussion of this development aimed to attract the attention of condensed matter community to this fascinating subject.
Cite
@article{arxiv.cond-mat/0309292,
title = {The Loewner equation: maps and shapes},
author = {Ilya A. Gruzberg and Leo P. Kadanoff},
journal= {arXiv preprint arXiv:cond-mat/0309292},
year = {2007}
}