The dimension of the SLE curves

Vincent Beffara

doi:10.1214/07-AOP364

The dimension of the SLE curves

Probability 2008-08-28 v3 Complex Variables

Authors: Vincent Beffara

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Abstract

Let $\gamma$ be the curve generating a Schramm--Loewner Evolution (SLE) process, with parameter $\kappa\geq0$ . We prove that, with probability one, the Hausdorff dimension of $\gamma$ is equal to $\operatorname {Min}(2,1+\kappa/8)$ .

Cite

@article{arxiv.math/0211322,
  title  = {The dimension of the SLE curves},
  author = {Vincent Beffara},
  journal= {arXiv preprint arXiv:math/0211322},
  year   = {2008}
}

Comments

Published in at http://dx.doi.org/10.1214/07-AOP364 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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