- 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
- Publisher copy:
- 10.1214/EJP.v19-2806
-
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- 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:
- Copyright date:
- 2012
- Notes:
- 21 pages
General item
Stochastic Domination and Comb Percolation
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