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

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

2008-12-08

arxiv.org/abs/0812.1384v2

Mathematics

Probability

9 pages and one figure

Scientific paper

10.1063/1.2840460

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.

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