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Stochastic Domination and Comb Percolation

Abstract:
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.
Publication status:
Published

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Publisher copy:
10.1214/EJP.v19-2806

Authors


Volume:
19
Issue:
0
Pages:
1-16
Publication date:
2012-01-30
DOI:
EISSN:
1083-6489
ISSN:
1083-6489
URN:
uuid:7a636153-53be-4807-9266-d7edff52b545
Source identifiers:
365331
Local pid:
pubs:365331
Language:
English
Keywords:

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