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Lecture Notes on Random Geometric Models --- Random Graphs, Point Processes and Stochastic Geometry

Bartłomiej Błaszczyszyn 1
1 DYOGENE - Dynamics of Geometric Networks
DI-ENS - Département d'informatique de l'École normale supérieure, CNRS - Centre National de la Recherche Scientifique : UMR 8548, Inria de Paris
Abstract : The goal of these lessons is to provide a quick access to some popular models of random geometric structures arising in a number of used in applications: communication networks (including social, transportation and wireless networks), geology, material sciences and astronomy. The course is composed of the following 15 lectures: (1) Bond percolation on the square lattice, (2) Galton-Watson tree, (3) Erdos-Renyi graph --- emergence of the giant component, (4) Graphs with a given node degree distribution, (5) Typical nodes and random unimodular graphs, (6) Erdos-Renyi graph --- emergence of the full connectivity, (7) Poisson point process, (8) Point conditioning and Palm theory for point processes, (9) Hard-core point processes, (10) Stationary point processes and mass transport principle, (11) Stationary Voronoi tessellation, (12) Ergodicity and point-shift invariance, (13) Random closed sets, (14) Boolean model and coverage processes, (15) Connectedness of random sets and continuum percolation. Usually, these topics are treated in distinct monographs: random graphs (lessons 2--6), point processes (7-12), stochastic geometry (13-14), where the percolation models presented in lesson 1 and 15 are often addressed separately. Gathering them in a single course provides an opportunity to observe some similarities and even fundamental relations between different models.
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Bartłomiej Błaszczyszyn. Lecture Notes on Random Geometric Models --- Random Graphs, Point Processes and Stochastic Geometry. Doctoral. Japan. 2017, pp.1-199. ⟨cel-01654766v1⟩

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