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V. Tassion (2014)
Crossing probabilities for Voronoi percolationarXiv: Probability
T. Liggett, R. Schonmann, A. Stacey (1997)
Domination by product measuresAnnals of Probability, 25
K. Alexander (1995)
Percolation and minimal spanning forests in infinite graphsAnnals of Probability, 23
Hugo Duminil, V. Sidoravicius, V. Tassion (2014)
Absence of Infinite Cluster for Critical Bernoulli Percolation on SlabsCommunications on Pure and Applied Mathematics, 69
R. Lyons, Y. Peres, O. Schramm (2004)
Minimal spanning forestsAnnals of Probability, 34
Thomas Sundal (2010)
Properties of minimum spanning trees and fractional quantum Hall states
H. Kesten (1987)
Scaling relations for 2D-percolationCommunications in Mathematical Physics, 109
(1999)
Percolation, volume 321
H. Duminil-Copin, V. Sidoravicius, V. Tassion (2015)
Continuity of the Phase Transition for Planar Random-Cluster and Potts Models with $${1 \le q \le 4}$$1≤q≤4Communications in Mathematical Physics, 349
(1999)
Grundlehren der mathematischen Wissenschaften, 321
Robin Pemantle (1991)
Choosing a Spanning Tree for the Integer Lattice UniformlyAnnals of Probability, 19
Olle Häggström (1995)
Random-cluster measures and uniform spanning treesStochastic Processes and their Applications, 59
I. Benjamini, R. Lyons, Y. Peres, O. Schramm (2001)
Uniform spanning forestsAnnals of Probability, 29
H. Kesten (1982)
Percolation theory for mathematicians
R. Burton, M. Keane (1989)
Density and uniqueness in percolationCommunications in Mathematical Physics, 121
M. Aizenman, H. Kesten, C. Newman (1987)
Uniqueness of the infinite cluster and continuity of connectivity functions for short and long range percolationCommunications in Mathematical Physics, 111
L. Russo (1978)
A note on percolationZeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 43
P. Seymour, D. Welsh (1978)
Percolation probabilities on the square latticeAnnals of discrete mathematics, 3
S. Smirnov (2001)
Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limitsComptes Rendus De L Academie Des Sciences Serie I-mathematique, 333
The phase transition in planar continuum percolation models
C. Newman, D. Stein (1994)
Spin-glass model with dimension-dependent ground state multiplicity.Physical review letters, 72 14
K. Alexander, S. Molchanov (1994)
Percolation of level sets for two-dimensional random fields with lattice symmetryJournal of Statistical Physics, 77
C. Newman, D. Stein (1995)
Ground-state structure in a highly disordered spin-glass modelJournal of Statistical Physics, 82
D. Wilson (1996)
Generating random spanning trees more quickly than the cover time
P. Balister, B. Bollobás, M. Walters (2005)
Continuum percolation with steps in the square or the discRandom Structures & Algorithms, 26
D. Basu, A. Sapozhnikov (2015)
Crossing probabilities for critical Bernoulli percolation on slabsarXiv: Probability
H. Duminil-Copin, V. Sidoravicius, V. Tassion (2016)
Continuity of the Phase Transition for Planar Random-Cluster and Potts Models with 1≤q≤4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}Communications in Mathematical Physics, 349
J. Chayes, L. Chayes, C. Newman (1985)
The stochastic geometry of invasion percolationCommunications in Mathematical Physics, 101
The minimal spanning forest on ℤd is known to consist of a single tree for d ≤ 2 and is conjectured to consist of infinitely many trees for large d. In this paper, we prove that there is a single tree for quasi‐planar graphs such as ℤ2 × {0,…,k}d−2. Our method relies on generalizations of the “gluing lemma” of Duminil‐Copin, Sidoravicius, and Tassion. A related result is that critical Bernoulli percolation on a slab satisfies the box‐crossing property. Its proof is based on a new Russo‐Seymour‐Welsh‐type theorem for quasi‐planar graphs. Thus, at criticality, the probability of an open path from 0 of diameter n decays polynomially in n. This strengthens the result of Duminil‐Copin et al., where the absence of an infinite cluster at criticality was first established. © 2017 Wiley Periodicals, Inc.
Communications on Pure & Applied Mathematics – Wiley
Published: Nov 1, 2017
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