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The Loewner equation: maps and shapes

Ilya A. Gruzberg·Leo P. Kadanoff
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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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Ilya A. Gruzberg, Leo P. Kadanoff. 2003-09-11. The Loewner equation: maps and shapes. https://doi.org/10.1023/b%3Ajoss.0000013973.40984.3b

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