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arXiv · 0812.1384

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

Yu Zhang
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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.

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Yu Zhang. 2008-12-25. A simple proof of exponential decay in the two dimensional percolation model. https://doi.org/10.1063/1.2840460

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