A Note on Large Deviations for the Stable Marriage of Poisson and Lebesgue with Random Appetites

Let Ξ ⊂ℝ d be a set of centers chosen according to a Poisson point process in ℝ d . Let ψ be an allocation of ℝ d to Ξ in the sense of the Gale–Shapley marriage problem, with the additional feature that every center ξ ∈ Ξ has an appetite given by a nonnegative random variable α . Generalizing some p...

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Bibliographic Details
Published in:Journal of theoretical probability 2012-03, Vol.25 (1), p.77-91
Main Author: Díaz Pachón, Daniel Andrés
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Statistics
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Summary:Let Ξ ⊂ℝ d be a set of centers chosen according to a Poisson point process in ℝ d . Let ψ be an allocation of ℝ d to Ξ in the sense of the Gale–Shapley marriage problem, with the additional feature that every center ξ ∈ Ξ has an appetite given by a nonnegative random variable α . Generalizing some previous results, we study large deviations for the distance of a typical point x ∈ℝ d to its center ψ ( x )∈ Ξ , subject to some restrictions on the moments of  α .
ISSN:0894-9840
1572-9230
DOI:10.1007/s10959-010-0304-9