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2014 Stochastic domination and comb percolation
Alexander Holroyd, James Martin
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Electron. J. Probab. 19: 1-16 (2014). DOI: 10.1214/EJP.v19-2806

Abstract

There exists a Lipschitz embedding of a d-dimensional comb graph (consisting of infinitely many parallel copies of $\mathbb{Z}^{d-1}$ joined by a perpendicular copy) into the open set of site percolation on $\mathbb{Z}^d$, whenever the parameter p is close enough to 1 or the Lipschitz constant is sufficiently large. This is proved using several new results and techniques involving stochastic domination, in contexts that include a process of independent overlapping intervals on $\mathbb{Z}$, and first-passage percolation on general graphs.

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Alexander Holroyd. James Martin. "Stochastic domination and comb percolation." Electron. J. Probab. 19 1 - 16, 2014. https://doi.org/10.1214/EJP.v19-2806

Information

Accepted: 8 January 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1291.60204
MathSciNet: MR3164758
Digital Object Identifier: 10.1214/EJP.v19-2806

Subjects:
Primary: 60K35
Secondary: 82B43

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