Discrete Loewner evolution

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.

21 pages

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