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

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Abstract

Let Ξ be a set of centres chosen according to a Poisson point process in. Consider the allocation of ℝ d to Ξ which is stable in the sense of the Gale-Shapley marriage problem, with the additional feature that every centre ξ ∈ Ξ has a random appetite, αV, where is a non-negative scale constant and V is a non-negative random variable. Generalizing previous results by Freire et al. (Stoch. Proc. Appl. 117(4) (2007), pp. 514-525), we show the absence of percolation when is small enough, depending on certain characteristics of the moment of V.

Original languageEnglish (US)
Pages (from-to)252-261
Number of pages10
JournalStochastics
Volume85
Issue number2
DOIs
StatePublished - Apr 2013

Keywords

  • percolation
  • Poisson process
  • random appetite
  • stable marriage

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation

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