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Discrete Loewner evolution

Robert O. Bauer
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Abstract

We study a one parameter family of discrete Loewner evolutions driven by a random walk on the real line. We show that it converges to the stochastic Loewner evolution (SLE) under rescaling. We show that the discrete Loewner evolution satisfies Markovian-type and symmetry properties analogous to SLE, and establish a phase transition property for the discrete Loewner evolution when the parameter equals 4.

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Robert O. Bauer. 2003-03-11. Discrete Loewner evolution. https://arxiv.org/abs/math/0303119

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