A simple proof of exponential decay in the two dimensional percolation model
arXiv:0812.1384 · doi:10.1063/1.2840460
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 $p_c=0.5$ 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.
9 pages and one figure