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One-arm exponent for critical 2D percolation

Gregory F. Lawler·Oded Schramm·Wendelin Werner
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Abstract

The probability that the cluster of the origin in critical site percolation on the triangular grid has diameter larger than $R$ is proved to decay like $R^{-5/48}$ as $R\to\infty$.

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Gregory F. Lawler, Oded Schramm, Wendelin Werner. 2001-08-30. One-arm exponent for critical 2D percolation. https://arxiv.org/abs/math/0108211

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