Random Geometric Graphs

Zusatztext 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. Klappentext This monograph provides and explains the mathematics behind geometric graph theory, which studies the properties of a graph that consists of nodes placed in Euclidean space so that edges can be added to connect points that are close to one another. For example, a collection of trees scattered in a forest and the disease that is passed between them, a set of nests of animals or birds on a region and the communication between them or communication between communications stations or nerve cells. Aimed at graduate students and researchers in probability, statistics, combinatorics and graph theory including computer scientists, it covers topics such as: technical tools, edge and component counts, vertex degrees, clique and chromatic number, and connectivity. Applications of this theory are used in the study of neural networks, spread of disease, astrophysics and spatial statistics. Zusammenfassung 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. Inhaltsverzeichnis 1: 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 ...

Klappentext
This monograph provides and explains the mathematics behind geometric graph theory, which studies the properties of a graph that consists of nodes placed in Euclidean space so that edges can be added to connect points that are close to one another. For example, a collection of trees scattered in a forest and the disease that is passed between them, a set of nests of animals or birds on a region and the communication between them or communication between communications stations or nerve cells. Aimed at graduate students and researchers in probability, statistics, combinatorics and graph theory including computer scientists, it covers topics such as: technical tools, edge and component counts, vertex degrees, clique and chromatic number, and connectivity. Applications of this theory are used in the study of neural networks, spread of disease, astrophysics and spatial statistics.


Zusammenfassung
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.

Inhalt
1: 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

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