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Cours Année : 2017

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

Résumé

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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Dates et versions

cel-01654766 , version 1 (04-12-2017)
cel-01654766 , version 2 (13-02-2020)
cel-01654766 , version 3 (02-03-2020)

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  • HAL Id : cel-01654766 , version 1

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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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