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

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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.

Original languageEnglish (US)
Pages (from-to)77-91
Number of pages15
JournalJournal of Theoretical Probability
Volume25
Issue number1
DOIs
StatePublished - Mar 2012
Externally publishedYes

Keywords

  • Large deviations
  • Poisson process
  • Random appetite
  • Stable marriage

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

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