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

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  • Daniel Andrés Díaz Pachón

    (Sao Paulo University)

Abstract

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.

Suggested Citation

  • Daniel Andrés Díaz Pachón, 2012. "A Note on Large Deviations for the Stable Marriage of Poisson and Lebesgue with Random Appetites," Journal of Theoretical Probability, Springer, vol. 25(1), pages 77-91, March.
    • Handle: RePEc:spr:jotpro:v:25:y:2012:i:1:d:10.1007_s10959-010-0304-9
    DOI: 10.1007/s10959-010-0304-9
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