Continuum AB percolation and AB random geometric graphs
نویسندگان
چکیده
منابع مشابه
Percolation and Connectivity in AB Random Geometric Graphs
Given two independent Poisson point processes Φ(1),Φ(2) in Rd, the AB Poisson Boolean model is the graph with points of Φ(1) as vertices and with edges between any pair of points for which the intersection of balls of radius 2r centred at these points contains at least one point of Φ(2). This is a generalization of the AB percolation model on discrete lattices. We show the existence of percolat...
متن کاملBootstrap Percolation on Random Geometric Graphs
Bootstrap percolation has been used effectively to model phenomena as diverse as emergence of magnetism in materials, spread of infection, diffusion of software viruses in computer networks, adoption of new technologies, and emergence of collective action and cultural fads in human societies. It is defined on an (arbitrary) network of interacting agents whose state is determined by the state of...
متن کاملBootstrap Percolation on Geometric Inhomogeneous Random Graphs
Geometric inhomogeneous random graphs (GIRGs) are a model for scale-free networks with underlying geometry. We study bootstrap percolation on these graphs, which is a process modelling the spread of an infection of vertices starting within a (small) local region. We show that the process exhibits a phase transition in terms of the initial infection rate in this region. We determine the speed of...
متن کاملOn AB bond percolation on the square lattice and AB site percolation on its line graph
We prove that AB site percolation occurs on the line graph of the square lattice when p ∈ (1− √ 1− pc, √ 1− pc), where pc is the critical probability for site percolation in Z. Also, we prove that AB bond percolation does not occur on Z for p = 1 2 .
متن کاملPercolation, connectivity, coverage and colouring of random geometric graphs
In this review paper, we shall discuss some recent results concerning several models of random geometric graphs, including the Gilbert disc model Gr , the k-nearest neighbour model G nn k and the Voronoi model GP . Many of the results concern finite versions of these models. In passing, we shall mention some of the applications to engineering and biology.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Applied Probability
سال: 2014
ISSN: 0021-9002,1475-6072
DOI: 10.1017/s0021900200021367