Skip to Main content Skip to Navigation

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

Bartłomiej Błaszczyszyn 1
1 DYOGENE - Dynamics of Geometric Networks
Inria de Paris, CNRS - Centre National de la Recherche Scientifique : UMR 8548, DI-ENS - Département d'informatique - ENS 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.
Document type :
Complete list of metadata

Cited literature [84 references]  Display  Hide  Download
Contributor : Bartlomiej Blaszczyszyn Connect in order to contact the contributor
Submitted on : Monday, March 2, 2020 - 4:44:09 PM
Last modification on : Friday, January 21, 2022 - 3:19:55 AM


Files produced by the author(s)


  • HAL Id : cel-01654766, version 3



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



Les métriques sont temporairement indisponibles