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The Loewner equation: maps and shapes

2003/09/11 by Ilya A. Gruzberg, Leo P. Kadanoff · 1 citation
Physics and Astronomy · #cond-mat.stat-mech

paper · pdf · doi:10.1023/b:joss.0000013973.40984.3b

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

arxiv created 2003/09/11 · arxiv updated 2009/12/01

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.

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