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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 - ENS Paris, 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. Erdős-Rényi graph — emergence of the giant component 4. Graphs with a given node degree distribution 5. Typical nodes and random unimodular graphs 6. Erdős-Rényi 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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Submitted on : Thursday, February 13, 2020 - 1:19:02 PM
Last modification on : Tuesday, January 11, 2022 - 11:16:03 AM


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  • HAL Id : cel-01654766, version 2


Bartłomiej Błaszczyszyn. Lecture Notes on Random Geometric Models --- Random Graphs, Point Processes and Stochastic Geometry. Doctoral. Japan. 2017, pp.1-199. ⟨cel-01654766v2⟩



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