Power Law Condition for Stability of Poisson Hail

Serguei Foss, Takis Konstantopoulos, Thomas Mountford

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
37 Downloads (Pure)


The Poisson hail model is a space-time stochastic system introduced by Baccelli and Foss (J Appl Prob 48A:343–366, 2011) whose stability condition is nonobvious owing to the fact that it is spatially infinite. Hailstones arrive at random points of time and are placed in random positions of space. Upon arrival, if not prevented by previously accumulated stones, a stone starts melting at unit rate. When the stone sizes have exponential tails, then stability conditions exist. In this paper, we look at heavy tailed stone sizes and prove that the system can be stabilized when the rate of arrivals is sufficiently small. We also show that the stability condition is, in a weak sense, optimal. We use techniques and ideas from greedy lattice animals.

Original languageEnglish
Pages (from-to)684-704
Number of pages21
JournalJournal of Theoretical Probability
Issue number2
Early online date24 Nov 2016
Publication statusPublished - Jun 2018


  • Greedy lattice animals
  • Poisson hail
  • Stability
  • Workload

ASJC Scopus subject areas

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


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