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Near critical scaling relations for planar Bernoulli percolation without differential inequalities

Hugo Duminil‐Copin et al.

Annals of Probability2026https://doi.org/10.1214/24-aop1755preprint
ABDC A*
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0.40

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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https://doi.org/https://doi.org/10.1214/24-aop1755

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@article{hugo2026,
  title        = {{Near critical scaling relations for planar Bernoulli percolation without differential inequalities}},
  author       = {Hugo Duminil‐Copin et al.},
  journal      = {Annals of Probability},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1214/24-aop1755},
}

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Near critical scaling relations for planar Bernoulli percolation without differential inequalities

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0.40

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.25 × 0.4 = 0.10
M · momentum0.53 × 0.15 = 0.08
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

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