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.
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 language | English |
|---|---|
| Pages (from-to) | 525-543 |
| Number of pages | 19 |
| Journal | Advances in Applied Probability |
| Volume | 48 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 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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Sergey Foss
- School of Mathematical & Computer Sciences - Professor
- School of Mathematical & Computer Sciences, Actuarial Mathematics & Statistics - Professor
Person: Academic (Research & Teaching)