Holroyd, Alexander E.; Martin, James B. Stochastic domination and comb percolation. (English) Zbl 1291.60204 Electron. J. Probab. 19, Paper No. 5, 16 p. (2014). Summary: 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. Cited in 5 Documents MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82B43 Percolation Keywords:stochastic domination; percolation; comb graph; Lipschitz embedding; first-passage percolation × Cite Format Result Cite Review PDF Full Text: DOI arXiv