منابع مشابه
Bootstrap Percolation on Periodic Trees
We study bootstrap percolation with the threshold parameter θ ≥ 2 and the initial probability p on infinite periodic trees that are defined as follows. Each node of a tree has degree selected from a finite predefined set of non-negative integers, and starting from a given node, called root, all nodes at the same graph distance from the root have the same degree. We show the existence of the cri...
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Bootstrap percolation on a graph G is defined as the spread of activation or infection according to the following rule, with a given threshold r ≥ 2: We start with a set A(0) ⊆ V (G) of active vertices. Each inactive vertex that has at least r active neigbours becomes active. This is repeated until no more vertices become active, i.e., when no inactive vertex has r or more active neigbours. We ...
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Bootstrap percolation is a general representation of some networked activation process, which has found applications in explaining many important social phenomena, such as the propagation of information. Inspired by some recent findings on spatial structure of online social networks, here we study bootstrap percolation on undirected spatial networks, with the probability density function of lon...
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In majority bootstrap percolation on a graph G, an infection spreads according to the following deterministic rule: if at least half of the neighbours of a vertex v are already infected, then v is also infected, and infected vertices remain infected forever. Percolation occurs if eventually every vertex is infected. The elements of the set of initially infected vertices, A ⊂ V (G), are normally...
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ژورنال
عنوان ژورنال: The Annals of Applied Probability
سال: 2015
ISSN: 1050-5164
DOI: 10.1214/13-aap996