Merging percolation and classical random graphs: Phase transition in dimension 1

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dc.creatorTurova, Tatyana S.
dc.creatorVallier, Thomas
dc.date2006-09-21
dc.date.accessioned2026-07-07T07:25:04Z
dc.date.available2026-07-07T07:25:04Z
dc.descriptionWe study a random graph model which combines properties of the edge percolation model on Z^d and a classical random graph G(n,c/n). We show that this model, being a homogeneous random graph, has a natural relation to the so-called "rank 1 case" of inhomogeneous random graphs. This allows us to use the newly developed theory of inhomogeneous random graphs to describe completely the phase diagram in the case d=1. The phase transition is similar to the classical random graph, it is of the second order. We also find the scaled size of the largest connected component above the phase transition.
dc.description24 pages
dc.identifierhttps://arxiv.org/abs/math/0609594
dc.identifierhttp://arxiv.org/abs/math/0609594
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/116601
dc.subjectProbability
dc.subject60C05, 05C80
dc.titleMerging percolation and classical random graphs: Phase transition in dimension 1
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