A percolating hard sphere model

Cotar, Codina; Holroyd, Alexander E.; Revelle, David

doi:10.1002/rsa.20230

Cited by 3 publications

(2 citation statements)

References 8 publications

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“…Percolation threshold bounds are also applied in the study of related models. As examples, Cotar, Holroyd, and Revelle [7] used an upper bound for the hexagonal lattice site percolation threshold [28] to prove the existence of percolation in a Poisson hard sphere process, and Don [12] used a lower bound for the square lattice site percolation threshold [38] to produce a bound for the threshold of fractal percolation.…”

Section: Introductionmentioning

confidence: 99%

An upper bound for the bond percolation threshold of the cubic lattice by a growth process approach

Wierman

2021

J. Appl. Probab.

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We reduce the upper bound for the bond percolation threshold of the cubic lattice from 0.447 792 to 0.347 297. The bound is obtained by a growth process approach which views the open cluster of a bond percolation model as a dynamic process. A three-dimensional dynamic process on the cubic lattice is constructed and then projected onto a carefully chosen plane to obtain a two-dimensional dynamic process on a triangular lattice. We compare the bond percolation models on the cubic lattice and their projections, and demonstrate that the bond percolation threshold of the cubic lattice is no greater than that of the triangular lattice. Applying the approach to the body-centered cubic lattice yields an upper bound of 0.292 893 for its bond percolation threshold.

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Section: Introductionmentioning

confidence: 99%

An upper bound for the bond percolation threshold of the cubic lattice by a growth process approach

Wierman

2021

J. Appl. Probab.

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“…does not have an unbounded connected component. Interestingly, there does exist a stationary percolating hard-core system of (non-lilypond) grains on Φ, at least in high dimensions; see [2].…”

Section: Introductionmentioning

confidence: 99%

Percolation and limit theory for the poisson lilypond model

Penrose

2012

Random Struct Algorithms

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The lilypond model on a point process in d ‐space is a growth‐maximal system of non‐overlapping balls centred at the points. We establish central limit theorems for the total volume and the number of components of the lilypond model on a sequence of Poisson or binomial point processes on expanding windows. For the lilypond model over a homogeneous Poisson process, we give subexponentially decaying tail bounds for the size of the cluster at the origin. Finally, we consider the enhanced Poisson lilypond model where all the balls are enlarged by a fixed amount (the enhancement parameter), and show that for d > 1 the critical value of this parameter, above which the enhanced model percolates, is strictly positive. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012

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Iterated Gilbert mosaics

Baccelli

Tran

2022

Stochastic Processes and their Applications

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A percolating hard sphere model

Cited by 3 publications

References 8 publications

An upper bound for the bond percolation threshold of the cubic lattice by a growth process approach

An upper bound for the bond percolation threshold of the cubic lattice by a growth process approach

Percolation and limit theory for the poisson lilypond model

Iterated Gilbert mosaics

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