Advances in Applied Probability

Shape theorems for Poisson hail on a bivariate ground

François Baccelli, Héctor A. Chang-Lara, and Sergey Foss

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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.

Article information

Source
Adv. in Appl. Probab., Volume 48, Number 2 (2016), 525-543.

Dates
First available in Project Euclid: 9 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.aap/1465490761

Mathematical Reviews number (MathSciNet)
MR3511774

Zentralblatt MATH identifier
1342.60010

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 60F15: Strong theorems 60G55: Point processes

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

Citation

Baccelli, François; Chang-Lara, Héctor A.; Foss, Sergey. Shape theorems for Poisson hail on a bivariate ground. Adv. in Appl. Probab. 48 (2016), no. 2, 525--543. https://projecteuclid.org/euclid.aap/1465490761


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References

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