Lecture Notes on Random Geometric Models --- Random Graphs, Point Processes and Stochastic Geometry - CEL - Cours en ligne Accéder directement au contenu
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.
Fichier principal
Vignette du fichier
randgeo.pdf (8.23 Mo) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

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

Identifiants

  • HAL Id : cel-01654766 , version 1

Citer

Bartłomiej Błaszczyszyn. Lecture Notes on Random Geometric Models --- Random Graphs, Point Processes and Stochastic Geometry. Doctoral. Japan. 2017, pp.1-199. ⟨cel-01654766v1⟩
1932 Consultations
3351 Téléchargements

Partager

Gmail Mastodon Facebook X LinkedIn More