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One-arm exponent for critical 2D percolation

Probability 2007-05-23 v1 Mathematical Physics Complex Variables math.MP

Abstract

The probability that the cluster of the origin in critical site percolation on the triangular grid has diameter larger than RR is proved to decay like R5/48R^{-5/48} as RR\to\infty.

Keywords

Cite

@article{arxiv.math/0108211,
  title  = {One-arm exponent for critical 2D percolation},
  author = {Gregory F. Lawler and Oded Schramm and Wendelin Werner},
  journal= {arXiv preprint arXiv:math/0108211},
  year   = {2007}
}