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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Statistics Seminars: Percolation for the stable marriage of Poisson and Lebesgue

Presented by Marina Vachkovskaia, University of Campinas

4 October 2006 11:15 in CM107

Let~$\Xi$ be the set of points (we call the elements of~$\Xi$ centers) of Poisson process in~$\R^d$, $d\geq 2$, with unit intensity. Consider the allocation of~$\R^d$ to~$\Xi$ which is stable in the sense of Gale-Shapley marriage problem and in which each center claims a region of volume~$\alpha\leq 1$. We prove that there is no percolation in the set of claimed sites if~$\alpha$ is small enough, and that, for high dimensions, there is percolation in the set of claimed sites if~$\alpha<1$ is large enough.

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