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Shape theorems for Poisson hail on a bivariate ground

Part of: Stochastic processes Limit theorems Geometric probability and stochastic geometry

Published online by Cambridge University Press:  10 June 2016

François Baccelli ,
Héctor A. Chang-Lara  and
Sergey Foss
François Baccelli*
Affiliation:
University of Texas
Héctor A. Chang-Lara*
Affiliation:
Columbia University
Sergey Foss*
Affiliation:
Heriot-Watt University and Sobolev Institute of Mathematics, Novosibirsk
*
* Postal address: Department of Mathematics, University of Texas, Austin, TX 78712, USA. Email address: baccelli@math.utexas.edu
** Postal address: Department of Mathematics, Columbia University, 2990 Broadway, New York, NY 10027, USA. Email address: changlara@math.columbia.edu
*** Postal address: School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK. Email address: s.foss@hw.ac.uk
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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.

Keywords

Point process theoryPoisson rainstochastic geometryrandom closed settime and space growthshapequeueing theorymax-plus algebraheapsbranching processsub-additive ergodic theory

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry 60F15: Strong theorems 60G55: Point processes
Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue 2 , June 2016 , pp. 525 - 543
Copyright
Copyright © Applied Probability Trust 2016 

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References

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