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Scale-free percolation

Maria Deijfen;  Remco van der Hofstad;  Gerard Hooghiemstra — 2013

Annales de l'I.H.P. Probabilités et statistiques

We formulate and study a model for inhomogeneous long-range percolation on ℤ d . Each vertex x ∈ ℤ d is assigned a non-negative weight W x , where ( W x ) x ∈ ℤ d are i.i.d. random variables. Conditionally on the weights, and given two parameters α , λ g t ; 0 , the edges are independent and the probability that there is an edge between x and y is given by p x y = 1 - exp { - λ W x W y / | x - y | α } . The parameter λ is the percolation parameter, while α describes the long-range nature of the model. We focus on the degree distribution in the resulting graph, on whether there...

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