Stochastic Geometry: Boolean model and random geometric graphs

Abstract

Abstract. This paper collects the four contributions which were presented during the session devoted to Stochastic Geometry at the journées MAS 2014. It is focused in particular on several questions related to the transmission of information in a general sense in different random media. The underlying models include the Boolean model, simplicial complexes or geometric random graphs induced by a point process.Résumé. Cet article propose les quatre contributions présentées lors de la session Géométrie stochastique des journées MAS 2014. Il est centré en particulier sur plusieurs questions de transmission de l'information au sens très général dans différents milieux aléatoires. Les modèles sous-jacents sont notamment le modèle Booléen, des complexes simpliciaux ou des graphes géométriques aléatoires engendrés par un processus ponctuel.

Coverage estimation of multicast OFDM systems based on stochastic geometry

“…Stochastic geometry (SG) is a discipline of applied mathematics that studies spatial random patterns with emphasis on the theory of Point Processes (PP) [10]. The classic SG models are mainly based on the study of Poisson Point Processes (PPP) [11]. The simplest model is the Boolean (BM), which is composed of random balls centered at each point of the process [10].…”