Percolation in High Dimensions
1991; Wiley; Volume: s2-44; Issue: 2 Linguagem: Inglês
10.1112/jlms/s2-44.2.373
ISSN1469-7750
Autores Tópico(s)Limits and Structures in Graph Theory
ResumoJournal of the London Mathematical SocietyVolume s2-44, Issue 2 p. 373-384 Notes and papers Percolation in High Dimensions Daniel M. Gordon, Daniel M. Gordon Department of Computer Science, University of Georgia, Athens, Georgia 30602, USASearch for more papers by this author Daniel M. Gordon, Daniel M. Gordon Department of Computer Science, University of Georgia, Athens, Georgia 30602, USASearch for more papers by this author First published: October 1991 https://doi.org/10.1112/jlms/s2-44.2.373Citations: 9AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract Let pc(d) be the critical probability for percolation in Zd. It is shown that limd→∞ 2dpc(d) = 1. The proof uses the properties of a random subgraph of an m-ary d-dimensional cube. If each edge in this cube is included with probability greater than 1/2d(1−3/m), then, for large d, the cube will have a connected component of size cmd for some c > 0. This generalizes a result of Ajtai, Komlós and Szemerédi. Citing Literature Volumes2-44, Issue2October 1991Pages 373-384 RelatedInformation
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