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On Spatial Point Processes with Uniform Births and Deaths by Random Connection
Francois Baccelli, Fabien Mathieu, Ilkka Norros
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 cr…
The Boolean Model in the Shannon Regime: Three Thresholds and Related Asymptotics
Venkat Anantharam, François Baccelli
Consider a family of Boolean models, indexed by integers , where the -th model features a Poisson point process in of intensity with $ρ_n \…
On Scaling Limits of Power Law Shot-noise Fields
François Baccelli, Anup Biswas
This article studies the scaling limit of a class of shot-noise fields defined on an independently marked stationary Poisson point process and with a power law response function. U…
Zeros of random tropical polynomials, random polytopes and stick-breaking
Francois Baccelli, Ngoc Mai Tran
For , let be independent and identically distributed random variables with distribution with support . The number of zeros of the random…
Shape Theorems for Poisson Hail on a Bivariate Ground
François Baccelli, Héctor A. Chang-Lara, Sergey Foss
We consider the extension of the Euclidean stochastic geometry Poisson Hail model to the case where the service speed is zero in some subset of the Euclidean space and infinity in…