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Lectures Year : 2017

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

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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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Dates and 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 3

Cite

Bartłomiej Błaszczyszyn. Lecture Notes on Random Geometric Models --- Random Graphs, Point Processes and Stochastic Geometry. Doctoral. France. 2017, pp.193. ⟨cel-01654766v3⟩
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