A short proof of the Harris-Kesten Theorem

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dc.creatorBollobas, Bela
dc.creatorRiordan, Oliver
dc.date2004-10-15
dc.date2005-06-16
dc.date.accessioned2026-07-07T07:44:21Z
dc.date.available2026-07-07T07:44:21Z
dc.descriptionWe give a short proof of the fundamental result that the critical probability for bond percolation in the planar square lattice is equal to 1/2. The lower bound was proved by Harris, who showed in 1960 that percolation does not occur at $p=1/2$. The other, more difficult, bound was proved by Kesten, who showed in 1980 that percolation does occur for any $p>1/2$.
dc.description17 pages, 9 figures; typos corrected. To appear in the Bulletin of the London Mathematical Society
dc.identifierhttps://arxiv.org/abs/math/0410359
dc.identifierhttp://arxiv.org/abs/math/0410359
dc.identifierBulletin of the London Mathematical Society 38 (2006), 470--484.
dc.identifierdoi:10.1112/S002460930601842X
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/123165
dc.subjectProbability
dc.subjectCombinatorics
dc.subject60K35; 82B43
dc.titleA short proof of the Harris-Kesten Theorem
dc.typetext

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