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Percolation in invariant Poisson graphs with i.i.d. degrees

M. Deijfen ; Olle Häggström (Institutionen för matematiska vetenskaper, matematisk statistik) ; A. E. Holroyd
Arkiv for Matematik (0004-2080). Vol. 50 (2012), 1, p. 41-58.
[Artikel, refereegranskad vetenskaplig]

Let each point of a homogeneous Poisson process in R-d independently be equipped with a random number of stubs (half-edges) according to a given probability distribution mu on the positive integers. We consider translation-invariant schemes for perfectly matching the stubs to obtain a simple graph with degree distribution mu. Leaving aside degenerate cases, we prove that for any mu there exist schemes that give only finite components as well as schemes that give infinite components. For a particular matching scheme which is a natural extension of Gale-Shapley stable marriage, we give sufficient conditions on mu for the absence and presence of infinite components.

Nyckelord: stationary random graphs, prescribed iid degrees, nearest-neighbor, degree sequence

Denna post skapades 2012-09-20.
CPL Pubid: 163656


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Institutionen för matematiska vetenskaper, matematisk statistik (2005-2016)



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