@article{EJP2806,
author = {Alexander Holroyd and James Martin},
title = {Stochastic domination and comb percolation},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {19},
year = {2014},
keywords = {stochastic domination, percolation, comb graph, Lipschitz embedding, first-passage percolation},
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.},
pages = {no. 5, 1-16},
issn = {1083-6489},
doi = {10.1214/EJP.v19-2806},
url = {http://ejp.ejpecp.org/article/view/2806}}