On the four-arm exponent for 2D percolation at criticality

2020/08/04 by Berg, Jacob van den, Nolin, Pierre
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2008.01606

Abstract

For two-dimensional percolation at criticality, we discuss the inequality α₄ > 1 for the polychromatic four-arm exponent (and stronger versions, the strongest so far being α₄ ≥ 1 + (α₂)/(2), where α₂ denotes the two-arm exponent). We first briefly discuss five proofs (some of them implicit and not self-contained) from the literature. Then we observe that, by combining two of them, one gets a completely self-contained (and yet quite short) proof.

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