Local Bootstrap Percolation
نویسندگان
چکیده
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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ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2009
ISSN: 1083-6489
DOI: 10.1214/ejp.v14-607