Random Geometric Graphs
Series: Oxford Studies in Probability; 5;
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72 119 Ft
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Product details:
- Publisher OUP Oxford
- Date of Publication 1 May 2003
- ISBN 9780198506263
- Binding Hardback
- No. of pages344 pages
- Size 241x162x22 mm
- Weight 649 g
- Language English
- Illustrations numerous figures 0
Categories
Short description:
This monograph provides and explains the probability theory of geometric graphs. Applications of the theory include communications networks, classification, spatial statistics, epidemiology, astrophysics and neural networks.
MoreLong description:
This 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.
The 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.
Table of Contents:
Introduction
Probabilistic ingredients
Subgraph and component counts
Typical vertex degrees
Geometrical ingredients
Maximum degree, cliques and colourings
Minimum degree: laws of large numbers
Minimum degree: convergence in distribution
Percolative ingredients
Percolation and the largest component
The largest component for a binomial process
Ordering and partitioning problems
Connectivity and the number of components
References
Index
