Exponential decay of connection probabilities for subcritical Voronoi percolation in \(\mathbb{R}^d\)

DOI10.1007/s00440-018-0838-9zbMath1478.60259arXiv1705.07978OpenAlexW2963902600WikidataQ115607545 ScholiaQ115607545MaRDI QIDQ1729700

Hugo Duminil-Copin, Aran Raoufi, Vincent Tassion

Publication date: 28 February 2019

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.07978

zbMATH Keywords

subcritical Voronoi percolation

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Percolation (82B43) Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics (82B21)

Related Items (20)

Annealed scaling relations for Voronoi percolation ⋮ The critical threshold for Bargmann-Fock percolation ⋮ The sharp phase transition for level set percolation of smooth planar Gaussian fields ⋮ New critical exponent inequalities for percolation and the random cluster model ⋮ Equality of critical parameters for percolation of Gaussian free field level sets ⋮ Slightly supercritical percolation on non‐amenable graphs I: The distribution of finite clusters ⋮ Phase transitions and noise sensitivity on the Poisson space via stopping sets and decision trees ⋮ Upper bounds on the one-arm exponent for dependent percolation models ⋮ Smooth Gaussian fields and percolation ⋮ Subcritical phase of \(d\)-dimensional Poisson-Boolean percolation and its vacant set ⋮ Continuum percolation in stochastic homogenization and the effective viscosity problem ⋮ Lectures on the Ising and Potts Models on the Hypercubic Lattice ⋮ Connection probabilities in Poisson random graphs with uniformly bounded edges ⋮ The annealed spectral sample of Voronoi percolation ⋮ Sharp phase transition for the continuum Widom-Rowlinson model ⋮ Sharpness of the phase transition for the orthant model ⋮ Criticality and covered area fraction in confetti and Voronoi percolation ⋮ Statistical physics on a product of trees ⋮ Equivalence of some subcritical properties in continuum percolation ⋮ Sharp threshold for two-dimensional majority dynamics percolation

Cites Work

• A new proof of the sharpness of the phase transition for Bernoulli percolation and the Ising model
• Crossing probabilities for Voronoi percolation
• The self-dual point of the two-dimensional random-cluster model is critical for \(q \geqslant 1\)
• Quenched Voronoi percolation
• Conformal invariance of Voronoi percolation
• A new computation of the critical point for the planar random-cluster model with \(q\geq1\)
• Sharp phase transition for the random-cluster and Potts models via decision trees
• Sharpness of the phase transition in percolation models
• The critical probability for random Voronoi percolation in the plane is 1/2
• Percolation
• Every monotone graph property has a sharp threshold
• Continuum Percolation
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