One-arm exponent for critical 2D percolation
Preprint
Abstract
The probability that the cluster of the origin in critical site percolation on the triangular grid has diameter larger than $R$ is proved to decay like $R^{-5/48}$ as $R\to\infty$.
Keywords
All Related Versions
This publication has 10 references indexed in Scilit:
- Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limitsComptes Rendus de l'Académie des Sciences - Series I - Mathematics, 2001
- Critical exponents for two-dimensional percolationMathematical Research Letters, 2001
- A Percolation FormulaElectronic Communications in Probability, 2001
- Scaling limits of loop-erased random walks and uniform spanning treesIsrael Journal of Mathematics, 2000
- Path-Crossing Exponents and the External Perimeter in 2D PercolationPhysical Review Letters, 1999
- Conductivity exponent and backbone dimension in 2-d percolationPhysica A: Statistical Mechanics and its Applications, 1999
- Almost All Words Are Seen In Critical Site Percolation On The Triangular LatticeElectronic Journal of Probability, 1998
- Critical percolation in finite geometriesJournal of Physics A: General Physics, 1992
- Percolation Theory for Mathematicians.Journal of the Royal Statistical Society. Series A (General), 1984
- Magnetic exponents of the two-dimensional q-state Potts modelJournal of Physics A: General Physics, 1980