The Loewner equation: maps and shapes

Details The Loewner equation: maps and shapes The Loewner equation: maps and shapes

2003-09-11

arxiv.org/abs/cond-mat/0309292v1

J. Stat. Phys. 114, 1183 (2004)

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1023/B:JOSS.0000013973.40984.

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.

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