Near critical scaling relations for planar Bernoulli percolation without differential inequalities

2021/11/29 by Duminil-Copin, Hugo, Manolescu, Ioan, Tassion, Vincent · 1 citation
#60K35 #82B27 #82B43 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2111.14414

Abstract

We provide a new proof of the near-critical scaling relation β=ξ₁ν for Bernoulli percolation on the square lattice already proved by Kesten in 1987. We rely on a novel approach that does not invoke Russo's formula, but rather relates differences in crossing probabilities at different scales. The argument is shorter and more robust than previous ones and is more likely to be adapted to other models. The same approach may be used to prove the other scaling relations appearing in Kesten's work.

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