Percolation phase transition in weight-dependent random connection models. (December 2021)

• Record Type: Journal Article
• Authors: Gracar, Peter; Lüchtrath, Lukas; Mörters, Peter
• Is Part Of: Advances in applied probability. Volume 53:Number 4(2021)
• Page Start: 1090
• Page End: 1114
• Publication Date: 2021-12
• Subjects: Subcritical regime -- random geometric graph -- Boolean model -- scale-free percolation -- long-range percolation -- spatial network -- robustness -- age-based spatial preferential attachment; 60K35 -- 05C80; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2021.13
• Languages: English
• ISSNs: 0001-8678

Abstract

Abstract: We investigate spatial random graphs defined on the points of a Poisson process in d -dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point is assigned an independent weight. Given the weight and position of the points, we form an edge between any pair of points independently with a probability depending on the two weights of the points and their distance. Preference is given to short edges and connections to vertices with large weights. We characterize the parameter regime where there is a non-trivial percolation phase transition and show that it depends not only on the power-law exponent of the degree distribution but also on a geometric model parameter. We apply this result to characterize robustness of age-based spatial preferential attachment networks.