Stochastic Domination and Comb Percolation

Details Stochastic Domination and Comb Percolation Stochastic Domination and Comb Percolation

2012-01-30

arxiv.org/abs/1201.6373v1

Mathematics

Probability

21 pages

Scientific paper

There exists a Lipschitz embedding of a d-dimensional comb graph (consisting of infinitely many parallel copies of Z^{d-1} joined by a perpendicular copy) into the open set of site percolation on 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 Z, and first-passage percolation on general graphs.

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