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On Point Processes Defined by Angular Conditions on Delaunay Neighbors in the Poisson-Voronoi Tessellation
François Baccelli, Sanket S. Kalamkar
Consider a homogeneous Poisson point process of the Euclidean plane and its Voronoi tessellation. The present note discusses the properties of two stationary point processes associ…
A computational framework for evaluating the role of mobility on the propagation of epidemics on point processes
François Baccelli, Nithin Ramesan
This paper is focused on SIS (Susceptible-Infected-Susceptible) epidemic dynamics (also known as the contact process) on populations modelled by homogeneous Poisson point processes…
Nash equilibrium structure of Cox process Hotelling games
Venkat Anantharam, Francois Baccelli
We study an N-player game where a pure action of each player is to select a non-negative function on a Polish space supporting a finite diffuse measure, subject to a finite constra…
Replica-Mean-Field Limits of Fragmentation-Interaction-Aggregation Processes
François Baccelli, Michel Davydov, Thibaud Taillefumier
Network dynamics with point-process-based interactions are of paramount modeling interest. Unfortunately, most relevant dynamics involve complex graphs of interactions for which an…
On the Steady State of Continuous Time Stochastic Opinion Dynamics with Power Law Confidence
Jae Oh Woo, François Baccelli, Sriram Vishwanath
This paper introduces a class of non-linear and continuous-time opinion dynamics model with additive noise and state dependent interaction rates between agents. The model features…
Community Detection on Euclidean Random Graphs
Emmanuel Abbe, Francois Baccelli, Abishek Sankararaman
We study the problem of community detection (CD) on Euclidean random geometric graphs where each vertex has two latent variables: a binary community label and a valu…
Reach of Repulsion for Determinantal Point Processes in High Dimensions
François Baccelli, Eliza O'Reilly
Goldman [7] proved that the distribution of a stationary determinantal point process (DPP) can be coupled with its reduced Palm version such that there exists a point…
Iterated Gilbert Mosaics and Poisson Tropical Plane Curves
Francois Baccelli, Ngoc M. Tran
We propose an iterated version of the Gilbert model, which results in a sequence of random mosaics of the plane. We prove that under appropriate scaling, this sequence of mosaics c…
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…
On the Generating Functionals of a Class of Random Packing Point Processes
Tien Viet Nguyen, François Baccelli
Consider a symmetrical conflict relationship between the points of a point process. The Matérn type constructions provide a generic way of selecting a subset of this point process…
Queuing Networks with Varying Topology -- A Mean-Field Approach
François Baccelli, Alexandre Rybko, Senya Shlosman
We consider the queuing networks, which are made from servers, exchanging their positions. The customers, using the network, try to reach their destinations, which is complicated b…
Semi-infinite paths of the 2d-Radial Spanning Tree
François Baccelli, David Coupier, Viet Chi Tran
We study semi-infinite paths of the radial spanning tree (RST) of a Poisson point process in the plane. We first show that the expectation of the number of intersection points betw…
Generating Functionals of Random Packing Point Processes: From Hard-Core to Carrier Sensing
Nguyen Tien Viet, Francois Baccelli
In this paper we study the generating functionals of several random packing processes: the classical Matérn hard-core model; its extensions, the -Matérn models and the -…
Optimal Paths on the Space-Time SINR Random Graph
Francois Baccelli, Bartlomiej Blaszczyszyn, Mir Omid Haji Mirsadeghi
We analyze a class of Signal-to-Interference-and-Noise-Ratio (SINR) random graphs. These random graphs arise in the modeling packet transmissions in wireless networks. In contrast…
The radial spanning tree of a Poisson point process
Francois Baccelli, Charles Bordenave
We analyze a class of spatial random spanning trees built on a realization of a homogeneous Poisson point process of the plane. This tree has a simple radial structure with the ori…
Stationary flows and uniqueness of invariant measures
Francois Baccelli, Takis Konstantopoulos
In this short paper, we consider a quadruple ,where is a -algebra of subsets of , and is a measurable bijection from into itself that preserves the…
Moments and tails in monotone-separable stochastic networks
Francois Baccelli, Sergey Foss
A network belongs to the monotone separable class if its state variables are homogeneous and monotone functions of the epochs of the arrival process. This framework, which was firs…