Percolation in a Dependent Random Environment

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dc.contributor.authorJonasson, Johan
dc.contributor.authorMossel, Elchanan
dc.contributor.authorPeres, Yuval
dc.date2023-05-17T15:07:12.000
dc.date.accessioned2023-05-23T03:36:31Z
dc.date.available2023-05-23T03:36:31Z
dc.date.issued2000-07-01
dc.date.submitted2016-07-25T09:51:47-07:00
dc.description.abstractDraw planes in ℝ3 that are orthogonal to the x axis, and intersect the x axis at the points of a Poisson process with intensity λ; similarly, draw planes orthogonal to the y and z axes using independent Poisson processes (with the same intensity). Taken together, these planes naturally define a randomly stretched rectangular lattice. Consider bond percolation on this lattice where each edge of length is open with probability e−, and these events are independent given the edge lengths. We show that this model exhibits a phase transition: for large enough λ there is an infinite open cluster a.s., and for small λ all open clusters are finite a.s. We prove this result using the method of paths with exponential intersection tails, which is not applicable in two dimensions. The question whether the analogous process in the plane exhibits a phase transition is open.
dc.identifier.urihttps://repository.upenn.edu/handle/20.500.14332/47820
dc.legacy.articleid1166
dc.legacy.fields10.1002/1098-2418(200007)16:4<333::AID-RSA3>3.0.CO;2-C
dc.legacy.fulltexturlhttps://repository.upenn.edu/cgi/viewcontent.cgi?article=1166&amp;context=statistics_papers&amp;unstamped=1
dc.rightsThis is the peer reviewed version of the following article: Jonasson, J., Mossel, E. and Peres, Y. (2000), Percolation in a dependent random environment. Random Struct. Alg., 16: 333–343., which has been published in final form at doi: 10.1002/1098-2418(200007)16:4<333::AID-RSA3>3.0.CO;2-C. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving http://olabout.wiley.com/WileyCDA/Section/id-820227.html#terms.
dc.source.beginpage333
dc.source.endpage343
dc.source.issue434
dc.source.issue4
dc.source.journalStatistics Papers
dc.source.journaltitleRandom Structures & Algorithms
dc.source.peerreviewedtrue
dc.source.statuspublished
dc.source.volume16
dc.subject.otherStatistics and Probability
dc.titlePercolation in a Dependent Random Environment
dc.typeArticle
digcom.contributor.authorJonasson, Johan
digcom.contributor.authorMossel, Elchanan
digcom.contributor.authorPeres, Yuval
digcom.identifierstatistics_papers/434
digcom.identifier.contextkey8874780
digcom.identifier.submissionpathstatistics_papers/434
digcom.typearticle
dspace.entity.typePublication
upenn.schoolDepartmentCenterStatistics Papers
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