Unoriented first-passage percolation on the n-cube
نویسندگان
چکیده
منابع مشابه
UNORIENTED FIRST-PASSAGE PERCOLATION ON THE n-CUBE BY ANDERS MARTINSSON
The n-dimensional binary hypercube is the graph whose vertices are the binary n-tuples {0,1}n and where two vertices are connected by an edge if they differ at exactly one coordinate. We prove that if the edges are assigned independent mean 1 exponential costs, the minimum length Tn of a path from (0,0, . . . ,0) to (1,1, . . . ,1) converges in probability to ln(1 +√2)≈ 0.881. It has previously...
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Percolation with edge-passage probability p and first-passage percolation are studied for the n-cube Bn = {0, 1} with nearest neighbor edges. For oriented and unoriented percolation, p = e/n and p = 1/n are the respective critical probabilities. For oriented first-passage percolation with i.i.d. edge-passage times having a density of 1 near the origin, the percolation time (time to reach the op...
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Percolation with edge-passage probability p and first-passage percolation are studied for the n-cube Bn = {0, 1}n with nearest neighbor edges. For oriented and unoriented percolation, p = e/n and p = 1/n are the respective critical probabilities. For oriented first-passage percolation with i.i.d. edge-passage times having a density of 1 near the origin, the percolation time (time to reach the o...
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Inspired by biological evolution, we consider the following socalled accessibility percolation problem: The vertices of the unoriented ndimensional binary hypercube are assigned independent U(0, 1) weights, referred to as fitnesses. A path is considered accessible if fitnesses are strictly increasing along it. We prove that the probability that the global fitness maximum is accessible from the ...
متن کاملFirst passage percolation on the random graph
We study first passage percolation on the random graph Gp(N) with exponentially distributed weights on the links. For the special case of the complete graph this problem can be described in terms of a continuous time Markov chain and recursive trees. The Markov chain X(t) describes the number of nodes that can be reached from the initial node in time t. The recursive trees, which are uniform tr...
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ژورنال
عنوان ژورنال: The Annals of Applied Probability
سال: 2016
ISSN: 1050-5164
DOI: 10.1214/15-aap1155