English

A simple proof of exponential decay in the two dimensional percolation model

Probability 2009-11-13 v2

Abstract

Kesten showed the exponential decay of percolation probability in the subcritical phase for the two-dimensional percolation model. This result implies his celebrated computation that pc=0.5p_c=0.5 for bond percolation in the square lattice, and site percolation in the triangular lattice, respectively. In this paper, we present a simpler proof for Kesten's theorem.

Keywords

Cite

@article{arxiv.0812.1384,
  title  = {A simple proof of exponential decay in the two dimensional percolation model},
  author = {Yu Zhang},
  journal= {arXiv preprint arXiv:0812.1384},
  year   = {2009}
}

Comments

9 pages and one figure

R2 v1 2026-06-21T11:49:13.365Z