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Discrete Loewner evolution

Probability 2007-05-23 v1 Complex Variables

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.

Cite

@article{arxiv.math/0303119,
  title  = {Discrete Loewner evolution},
  author = {Robert O. Bauer},
  journal= {arXiv preprint arXiv:math/0303119},
  year   = {2007}
}

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21 pages