On Spatial Point Processes with Uniform Births and Deaths by Random Connection

Francois Baccelli 1, 2, 3 Fabien Mathieu 3, 4 Ilkka Norros 5
2 DYOGENE - Dynamics of Geometric Networks
DI-ENS - Département d'informatique de l'École normale supérieure, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR8548
Abstract : This paper is focused on a class of spatial birth and death process of the Euclidean space where the birth rate is constant and the death rate of a given point is the shot noise created at its location by the other points of the current configuration for some response function f. An equivalent view point is that each pair of points of the configuration establishes a random connection at an exponential time determined by f, which results in the death of one of the two points. We concentrate on space-motion invariant processes of this type. Under some natural conditions on f, we construct the unique time-stationary regime of this class of point processes by a coupling argument. We then use the birth and death structure to establish a hierarchy of balance integral relations between the factorial moment measures. Finally, we show that the time-stationary point process exhibits a certain kind of repulsion between its points that we call f-repulsion.
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https://hal.inria.fr/hal-01059857
Contributor : Fabien Mathieu <>
Submitted on : Tuesday, September 2, 2014 - 10:09:28 AM
Last modification on : Tuesday, May 14, 2019 - 10:16:00 AM

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  • HAL Id : hal-01059857, version 1
  • ARXIV : 1408.6888

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Francois Baccelli, Fabien Mathieu, Ilkka Norros. On Spatial Point Processes with Uniform Births and Deaths by Random Connection. [Research Report] 2014. ⟨hal-01059857⟩

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