Near critical scaling relations for planar Bernoulli percolation without differential inequalities
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.
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Theoretical and Computational Physics
Markov Chains and Monte Carlo Methods
Publication details
- Journal / source
- The Annals of Probability
- Publisher
- Institute of Mathematical Statistics
- Volume
- 54
- Issue
- 1
- Pages
- 137-154
- Publication date
- 1 January 2026
- Language
- EN