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Crossing Formulae for Critical Percolation in an Annulus

Mathematical Physics 2007-05-23 v4 Disordered Systems and Neural Networks math.MP Probability

Abstract

An exact formula is given for the probability that there exists a spanning cluster between opposite boundaries of an annulus, in the scaling limit of critical percolation. The entire distribution function for the number of distinct spanning clusters is also given. These results are found using Coulomb gas methods. Their forms are compared with the expectations of conformal field theory.

Keywords

Cite

@article{arxiv.math-ph/0208019,
  title  = {Crossing Formulae for Critical Percolation in an Annulus},
  author = {John Cardy},
  journal= {arXiv preprint arXiv:math-ph/0208019},
  year   = {2007}
}

Comments

7 pages, 1 figure; v.2,3: minor corrections; v.4: published version

R2 v1 2026-07-22T16:21:46.597Z