Crossing probabilities for planar percolation

DOI10.1215/00127094-2022-0015arXiv2011.04618OpenAlexW3100070096MaRDI QIDQ6042547

Vincent Tassion, Laurin Köhler-Schindler

Publication date: 11 May 2023

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.04618

zbMATH Keywords

criticalitypercolationcrossingRusso-Seymour-Welsh

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Probability in computer science (algorithm analysis, random structures, phase transitions, etc.) (68Q87)

Related Items (3)

The phase transition for planar Gaussian percolation models without FKG ⋮ Combinatorics, probability and computing. Abstracts from the workshop held April 24--30, 2022 ⋮ Smooth Gaussian fields and percolation

Cites Work

• Crossing probabilities for Voronoi percolation
• Continuity of the phase transition for planar random-cluster and Potts models with \({1 \leq q \leq 4}\)
• Percolation of random nodal lines
• The self-dual point of the two-dimensional random-cluster model is critical for \(q \geqslant 1\)
• The critical probability of bond percolation on the square lattice equals 1/2
• Correlation inequalities on some partially ordered sets
• Sharpness of the phase transition for continuum percolation in \(\mathbb{R}^2\)
• The box-crossing property for critical two-dimensional oriented percolation
• Crossing probabilities for critical Bernoulli percolation on slabs
• Discretisation schemes for level sets of planar Gaussian fields
• The scaling limits of near-critical and dynamical percolation
• The RSW theorem for continuum percolation and the CLT for Euclidean minimal spanning trees
• Scaling relations for 2D-percolation
• Russo-Seymour-Welsh estimates for the Kostlan ensemble of random polynomials
• Logarithmic variance for the height function of square-ice
• A short proof of the discontinuity of phase transition in the planar random-cluster model with \(q > 4\)
• Quasi-independence for nodal lines
• Liouville first-passage percolation: subsequential scaling limits at high temperature
• Emergent planarity in two-dimensional Ising models with finite-range interactions
• The critical probability for random Voronoi percolation in the plane is 1/2
• The Russo-Seymour-Welsh theorem and the equality of critical densities and the ``dual critical densities for continuum percolation on \({\mathbb{R}}^ 2\)
• Uniform Lipschitz functions on the triangular lattice have logarithmic variations
• Macroscopic loops in the loop \(O(n)\) model at Nienhuis' critical point
• Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits
• Absence of Infinite Cluster for Critical Bernoulli Percolation on Slabs
• Percolation on self-dual polygon configurations
• Lectures on the Ising and Potts Models on the Hypercubic Lattice
• Lectures on two-dimensional critical percolation
• Percolation
• On the critical percolation probabilities
• A note on percolation
• Percolation Probabilities on the Square Lattice
• Percolation
• Critical Percolation and the Minimal Spanning Tree in Slabs
• Discontinuity of the phase transition for the planar random-cluster and Potts models with $q>4$
• Renormalization of crossing probabilities in the planar random-cluster model
• Connection probabilities and RSW‐type bounds for the two‐dimensional FK Ising model
• A SHORT PROOF OF THE HARRIS–KESTEN THEOREM
• The Random-Cluster Model

This page was built for publication: Crossing probabilities for planar percolation