Results 1  10
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426
BOND PERCOLATION ON ISORADIAL GRAPHS
, 2012
"... In an investigation of percolation on isoradial graphs, we prove the criticality of canonical bond percolation on isoradial embeddings of planar graphs, thus extending celebrated earlier results for homogeneous and inhomogeneous square, triangular, and other lattices. This is achieved via the star– ..."
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In an investigation of percolation on isoradial graphs, we prove the criticality of canonical bond percolation on isoradial embeddings of planar graphs, thus extending celebrated earlier results for homogeneous and inhomogeneous square, triangular, and other lattices. This is achieved via the star
Universality for bond percolation in two dimensions
, 2011
"... Abstract. All (in)homogeneous bond percolation models on the square, triangular, and hexagonal lattices belong to the same universality class, in the sense that they have identical critical exponents at the critical point (assuming the exponents exist). This is proved using the star–triangle transfo ..."
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Cited by 4 (2 self)
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Abstract. All (in)homogeneous bond percolation models on the square, triangular, and hexagonal lattices belong to the same universality class, in the sense that they have identical critical exponents at the critical point (assuming the exponents exist). This is proved using the star
Estimation of bond percolation thresholds on the Archimedean lattices
 J. Phys. A
"... Abstract. We give accurate estimates for the bond percolation critical probabilities on seven Archimedean lattices, for which the critical probabilities are unknown, using an algorithm of Newman and Ziff. 1. ..."
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Cited by 5 (2 self)
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Abstract. We give accurate estimates for the bond percolation critical probabilities on seven Archimedean lattices, for which the critical probabilities are unknown, using an algorithm of Newman and Ziff. 1.
Critical probabilities for site and bond percolation models
 Annals of Probability
, 1998
"... Abstract.Any infinite graph G = (V, E) has a site percolation critical probability psite c and a bond percolation critical probability pbond c. The well known weak inequality psite c ≥ pbond c is strengthened to strict inequality for a broad category of graphs G, including all the usual finitedimen ..."
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Cited by 23 (1 self)
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Abstract.Any infinite graph G = (V, E) has a site percolation critical probability psite c and a bond percolation critical probability pbond c. The well known weak inequality psite c ≥ pbond c is strengthened to strict inequality for a broad category of graphs G, including all the usual finite
On AB bond percolation on the square lattice and AB
"... We prove that AB site percolation occurs on the line graph of the square lattice when p ∈ (1 − √ 1 − pc, √ 1 − pc), where pc is the critical probability for site percolation in Z 2. Also, we prove that AB bond percolation does not occur on Z 2 for p = 1 2. ..."
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We prove that AB site percolation occurs on the line graph of the square lattice when p ∈ (1 − √ 1 − pc, √ 1 − pc), where pc is the critical probability for site percolation in Z 2. Also, we prove that AB bond percolation does not occur on Z 2 for p = 1 2.
Brownian Bridge Asymptotics for the Subcritical Bernoulli Bond Percolation.
, 2008
"... For the ddimensional model of a subcritical bond percolation (p < pc) and a point ⃗a in Zd, we prove that a cluster conditioned on connecting points (0,...,0) and n⃗a if 1 1 scaled by n‖⃗a‖ along ⃗a and by √ in the orthogonal direction converges asymptotically n to Time × (d − 1)dimensional Bro ..."
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Cited by 3 (0 self)
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For the ddimensional model of a subcritical bond percolation (p < pc) and a point ⃗a in Zd, we prove that a cluster conditioned on connecting points (0,...,0) and n⃗a if 1 1 scaled by n‖⃗a‖ along ⃗a and by √ in the orthogonal direction converges asymptotically n to Time × (d − 1)dimensional
AN INVESTIGATION OF SITEBOND PERCOLATION ON MANY LATTICES
, 1999
"... A calculation of sitebond percolation thresholds in many lattices in two to five dimensions is presented. The line of threshold values has been parametrized in the literature, but we show here that there are strong deviations from the known approximate equations. We propose an alternative parametri ..."
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Cited by 2 (0 self)
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A calculation of sitebond percolation thresholds in many lattices in two to five dimensions is presented. The line of threshold values has been parametrized in the literature, but we show here that there are strong deviations from the known approximate equations. We propose an alternative
INHOMOGENEOUS BOND PERCOLATION ON SQUARE, TRIANGULAR, AND HEXAGONAL LATTICES
 SUBMITTED TO THE ANNALS OF PROBABILITY
, 2011
"... The star–triangle transformation is used to obtain an equivalence extending over the set of all (in)homogeneous bond percolation models on the square, triangular, and hexagonal lattices. Amongst the consequences are boxcrossing (RSW) inequalities for such models with parametervalues at which the t ..."
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Cited by 9 (3 self)
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The star–triangle transformation is used to obtain an equivalence extending over the set of all (in)homogeneous bond percolation models on the square, triangular, and hexagonal lattices. Amongst the consequences are boxcrossing (RSW) inequalities for such models with parametervalues at which
Bond Percolation Critical Probability Bounds for the Kagomé Lattice by a Substitution Method
"... A new substitution method improves bounds for critical probabilities of the bond percolation problem on the Kagome lattice, K. ..."
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Cited by 6 (6 self)
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A new substitution method improves bounds for critical probabilities of the bond percolation problem on the Kagome lattice, K.
Extraordinary Behavior in Correlated SiteBond Percolation
, 1997
"... Sitebond percolation is addressed in a very general class of correlated sitebond systems. The sitebond model analyzed provides a simple natural picture of disordered media such as porous materials, nonuniform surfaces adsorption potential, conductivity of inhomogeneous systems and landscapes. The ..."
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Sitebond percolation is addressed in a very general class of correlated sitebond systems. The sitebond model analyzed provides a simple natural picture of disordered media such as porous materials, nonuniform surfaces adsorption potential, conductivity of inhomogeneous systems and landscapes
Results 1  10
of
426