Shape theorems for Poisson hail on a bivariate ground

François Baccelli, Hector A. Chang-Lara, Sergey Foss

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1 Citation (Scopus)

Abstract

We consider an extension of the Poisson hail model where the service speed is
either 0 or∞ at each point of the Euclidean space. We use and develop tools pertaining to sub-additive ergodic theory in order to establish shape theorems for the growth of the ice-heap under light tail assumptions on the hailstone characteristics. The asymptotic shape depends on the statistics of the hailstones, the intensity of the underlying Poisson point process, and on the geometrical properties of the zero speed set.
Original languageEnglish
Pages (from-to)525-543
Number of pages19
JournalAdvances in Applied Probability
Volume48
Issue number2
DOIs
Publication statusPublished - Jun 2016

Keywords

  • Point process theory
  • random closed set
  • Poisson rain
  • stochastic geometry
  • time and space growth
  • shape
  • queueing theory
  • max-plus algebra
  • heaps
  • branching process
  • sub-additive ergodic theory

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