Connected Spatial Networks over Random Points and a Route-Length Statistic
نویسندگان
چکیده
منابع مشابه
Connected Spatial Networks over Random Points and a Route-Length Statistic
We review mathematically tractable models for connected networks on random points in the plane, emphasizing the class of proximity graphs which deserves to be better known to applied probabilists and statisticians. We introduce and motivate a particular statistic R measuring shortness of routes in a network. We illustrate, via Monte Carlo in part, the trade-off between normalized network length...
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We review mathematically tractable models for connected networks on random points in the plane, emphasising the little-studied class of proximity graphs and introducing a new model called the Hammersley network. We introduce and motivate a particular statistic R measuring shortness of routes in a network. We show (via Monte Carlo, in part) the trade-off between normalized network length and R i...
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For a connected network on Poisson points in the plane, consider the route-length D(r, θ) between a point near the origin and a point near polar coordinates (r, θ), and suppose ED(r, θ) = O(r) as r →∞. By analogy with the shape theorem for first-passage percolation, for a translation-invariant and ergodic network one expects r−1D(r, θ) to converge as r → ∞ to a constant ρ(θ). It turns out there...
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This note compares some current theoretical mathematical work on spatial networks with data on inter-city road networks within States. In designing a network, a natural constraint is the total length, and a natural objective is to want the route length `(i, j) between typical cities i, j to be not much longer than straight line distance d(i, j). Write r(i, j) = `(i,j) d(i,j) − 1 for the relativ...
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ژورنال
عنوان ژورنال: Statistical Science
سال: 2010
ISSN: 0883-4237
DOI: 10.1214/10-sts335