Stable Poisson Graphs in One Dimension
نویسندگان
چکیده
Let each point of a homogeneous Poisson process on R independently be equipped with a random number of stubs (half-edges) according to a given probability distribution μ on the positive integers. We consider two natural schemes for perfectly matching the stubs to obtain a simple graph with degree distribution μ, both derived from Gale-Shapley stable marriage. We prove results on the existence of an infinite component and on the length of the edges, with focus on the case μ({2}) = 1.
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