Percolation for the stable marriage of Poisson and Lebesgue with random appetites

Details Percolation for the stable marriage of Poisson and Lebesgue with random appetites Percolation for the stable marriage of Poisson and Lebesgue with random appetites

2009-09-29

arxiv.org/abs/0909.5325v4

Mathematics

Probability

12 pages. Substantially improved

Scientific paper

Let $\Xi$ be a set of centers chosen according to a Poisson point process in $\mathbb R^d$. Consider the allocation of $\mathbb R^d$ to $\Xi$ which is stable in the sense of the Gale-Shapley marriage problem, with the additional feature that every center $\xi\in\Xi$ has a random appetite $\alpha V$, where $\alpha$ is a nonnegative scale constant and $V$ is a nonnegative random variable. Generalizing previous results by Freire, Popov and Vachkovskaia (\cite{FPV}), we show the absence of percolation when $\alpha$ is small enough, depending on certain characteristics of the moment of $V$.

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