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.

Random Geometric Graphs (Oxford Studies in Probability)

Science & Math

Penrose, Mathew

Mathematics

Oxford University Press

Lectures on the Poisson Process (Institute of Mathematical Statistics Textbooks, Series Number 7)

The Poisson process, a core object in modern probability, enjoys a richer theory than is sometimes appreciated. This volume develops the theory in the setting of a general abstract measure space, establishing basic results and properties as well as certain advanced topics in the stochastic analysis of the Poisson process. Also discussed are applications and related topics in stochastic geometry, including stationary point processes, the Boolean model, the Gilbert graph, stable allocations, and hyperplane processes. Comprehensive, rigorous, and self-contained, this text is ideal for graduate courses or for self-study, with a substantial number of exercises for each chapter. Mathematical prerequisites, mainly a sound knowledge of measure-theoretic probability, are kept in the background, but are reviewed comprehensively in the appendix. The authors are well-known researchers in probability theory; especially stochastic geometry. Their approach is informed both by their research and by their extensive experience in teaching at undergraduate and graduate levels.

Last, Günter

Cambridge University Press

Random Graphs, Geometry and Asymptotic Structure (London Mathematical Society Student Texts, Series Number 84)

The theory of random graphs is a vital part of the education of any researcher entering the fascinating world of combinatorics. However, due to their diverse nature, the geometric and structural aspects of the theory often remain an obscure part of the formative study of young combinatorialists and probabilists. Moreover, the theory itself, even in its most basic forms, is often considered too advanced to be part of undergraduate curricula, and those who are interested usually learn it mostly through self-study, covering a lot of its fundamentals but little of the more recent developments. This book provides a self-contained and concise introduction to recent developments and techniques for classical problems in the theory of random graphs. Moreover, it covers geometric and topological aspects of the theory and introduces the reader to the diversity and depth of the methods that have been devised in this context.

Krivelevich, Michael

Panagiotou, Konstantinos

McDiarmid, Colin

The theory of random graphs is a vital part of the education of any researcher entering the fascinating world of combinatorics. However, due to their diverse nature, the geometric and structural aspects of the theory often remain an obscure part of the formative study of young combinatorialists and probabilists. Moreover, the theory itself, even in its most basic forms, is often considered too advanced to be part of undergraduate curricula, and those who are interested usually learn it mostly through self-study, covering a lot of its fundamentals but little of the more recent developments. This book provides a self-contained and concise introduction to recent developments and techniques for classical problems in the theory of random graphs. Moreover, it covers geometric and topological aspects of the theory and introduces the reader to the diversity and depth of the methods that have been devised in this context.

See the best price to sell, buy, or rent books by Penrose, Mathew. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Penrose, Mathew

See the best price to sell, buy, or rent books by Penrose, Mathew. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Random Geometric Graphs (Oxford Studies in Probability)

Lectures on the Poisson Process (Institute of Mathematical Statistics Textbooks, Series Number 7)

Random Graphs, Geometry and Asymptotic Structure (London Mathematical Society Student Texts, Series Number 84)

Lectures on the Poisson Process (Institute of Mathematical Statistics Textbooks, Series Number 7)

Random Graphs, Geometry and Asymptotic Structure (London Mathematical Society Student Texts, Series Number 84)