Random Geometric Graphs: 5 (Oxford Studies in Probability) - Hardcover

Penrose, Mathew

Hardcover

ISBN 10: 0198506260 ISBN 13: 9780198506263

Publisher: OUP Oxford, 2003

Synopsis

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.

About this title

Review

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. (Zentralblatt MATH)

About the Author

Peter Morters is a professor of probability at the University of Bath. Receiving his PhD from the University of London in the area of geometric measure theory, his current interests focus on Bronwnian motion and random walk, stohastic processes in random environments, large deviation theory and,
more recently random networks. Roger Moser is a lecturer of mathematics at the University of Bath. He received his PhD from the Eidgenossische Technische Hochschule Zurich in the area of geometric analysis. Further current research interests include the theory of partial differential equations, the
calculus of variations, geometric measure theory, and applications if mathematical phsyics. Mathew Penrose is a professor of Probability at the University of Bath. His current research interests are mainly in stohastic geometry and interacting particle systems. His monograph "Random Geometric
Graphs" was published by Oxford University Press in 2003. He obtained his PhD in stohastic analysis from the University of Edinburgh. Hartmut Schwetlick is a lecturer of mathematics at the University of Bath. After receiving his PhD from the University of Tubingen in the field of nonlinear transport
equations, he worked on partial differential equations and their applications at ETH Zurich and the Max Planck Institute for Mathematics in teh Sciences, Leipzig. His research interests include analysis of PDE, variational methods in geometric analysis, and nonlinear elasticity. Johannes Zimmer is
currently a lecturer of applied mathematics at the University of Bath.Prior to that, he was head of an Emmy Noether group at the Max Planck Institute for Mathematics in the Sciences, Leipzig. He obtainedhis doctorate from the Technische universitat Munchen. Research interests include the analysis
of lattice dynamical systems, and PDEs, continuum mechanics, and phase transitions.

Edition details

• Publisher: OUP Oxford
• Publication date: 2003
• Language: English
• ISBN 10: 0198506260
• ISBN 13: 9780198506263
• Binding: Hardcover
• Number of pages: 344