Description
Book SynopsisThis monograph sets out a body of mathematical theory for finite graphs with nodes placed randomly in Euclidean space and edges added to connect points that are close to each other. As an alternative to classical random graph models, these geometric graphs are relevant to the modelling of real-world networks having spatial content, arising in numerous applications such as wireless communications, parallel processing, classification, epidemiology, astronomy, and the internet. Aimed at graduate students and researchers in probability, combinatorics, statistics, and theoretical computer science, it covers topics such as edge and component counts, vertex degrees, cliques, colourings, connectivity, giant component phenomena, vertex ordering and partitioning problems. It also illustrates and extends the application to geometric probability of modern techniques including Stein''s method, martingale methods and continuum percolation.
Trade ReviewThe book is suitable to design a graduate course in random geometric graphs. Its scope stretches far beyond geometric probability and includes exciting material from Poisson approximation, percolation and statistical physics. This elegantly written monograph belongs to the collection of important books vital for every probabilist. * Zentralblatt MATH *
Table of Contents1. Introduction ; 2. Probabilistic ingredients ; 3. Subgraph and component counts ; 4. Typical vertex degrees ; 5. Geometrical ingredients ; 6. Maximum degree, cliques and colourings ; 7. Minimum degree: laws of large numbers ; 8. Minimum degree: convergence in distribution ; 9. Percolative ingredients ; 10. Percolation and the largest component ; 11. The largest component for a binomial process ; 12. Ordering and partitioning problems ; 13. Connectivity and the number of components ; References ; Index
