منابع مشابه
Local Bootstrap Percolation
We study a variant of bootstrap percolation in which growth is restricted to a single active cluster. Initially there is a single active site at the origin, while other sites of Z2 are independently occupied with small probability p, otherwise empty. Subsequently, an empty site becomes active by contact with two or more active neighbors, and an occupied site becomes active if it has an active s...
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Abstract. By bootstrap percolation we mean the following deterministic process on a graph G. Given a set A of vertices ‘infected’ at time 0, new vertices are subsequently infected, at each time step, if they have at least r ∈ N previously infected neighbours. When the set A is chosen at random, the main aim is to determine the critical probability pc(G, r) at which percolation (infection of the...
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In the bootstrap percolation model, sites in an L by L square are initially infected independently with probability p. At subsequent steps, a healthy site becomes infected if it has at least 2 infected neighbours. As (L, p) → (∞, 0), the probability that the entire square is eventually infected is known to undergo a phase transition in the parameter p log L, occurring asymptotically at λ = π2/1...
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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 models describe systems as diverse as magnetic materials, fluid flow in rocks and computer storage systems. The models have a common feature of requiring not just a simple connectivity of neighbouring sites, but rather an environment of other suitably occupied sites. Different applications as well as the connection with the mathematical literature on these models is presen...
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ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2009
ISSN: 1083-6489
DOI: 10.1214/ejp.v14-607