N ov 2 00 5 Percolation for the stable marriage of Poisson and Lebesgue
نویسندگان
چکیده
Let Ξ be the set of points (we call the elements of Ξ centers) of Poisson point process in Rd, d ≥ 2, with unit intensity. Consider the allocation of Rd to Ξ which is stable in the sense of Gale-Shapley marriage problem and in which each center claims a region of volume α ≤ 1. We prove that there is no percolation in the set of claimed sites if α is small enough, and that, for high dimensions, there is percolation in the set of claimed sites if α < 1 is large enough.
منابع مشابه
2 4 Ju l 2 00 6 Percolation for the stable marriage of Poisson and Lebesgue
Let Ξ be the set of points (we call the elements of Ξ centers) of Poisson process in Rd, d ≥ 2, with unit intensity. Consider the allocation of Rd to Ξ which is stable in the sense of Gale-Shapley marriage problem and in which each center claims a region of volume α ≤ 1. We prove that there is no percolation in the set of claimed sites if α is small enough, and that, for high dimensions, there ...
متن کاملar X iv : m at h / 05 11 18 6 v 2 [ m at h . PR ] 1 3 Ju l 2 00 6 Percolation for the stable marriage of Poisson and Lebesgue
Let Ξ be the set of points (we call the elements of Ξ centers) of Poisson process in Rd, d ≥ 2, with unit intensity. Consider the allocation of Rd to Ξ which is stable in the sense of Gale-Shapley marriage problem and in which each center claims a region of volume α ≤ 1. We prove that there is no percolation in the set of claimed sites if α is small enough, and that, for high dimensions, there ...
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