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E-raamat: Random Networks for Communication: From Statistical Physics to Information Systems

(Vrije Universiteit, Amsterdam), (University of California, San Diego)
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First rigorous introduction for graduate students and scientists to techniques and problems motivated by wireless data networks.

When is a random network (almost) connected? How much information can it carry? How can you find a particular destination within the network? And how do you approach these questions - and others - when the network is random? The analysis of communication networks requires a fascinating synthesis of random graph theory, stochastic geometry and percolation theory to provide models for both structure and information flow. This book is the first comprehensive introduction for graduate students and scientists to techniques and problems in the field of spatial random networks. The selection of material is driven by applications arising in engineering, and the treatment is both readable and mathematically rigorous. Though mainly concerned with information-flow-related questions motivated by wireless data networks, the models developed are also of interest in a broader context, ranging from engineering to social networks, biology, and physics.

Arvustused

'The balance between intuition and rigor is ideal, in my opinion, and reading the book is an enjoyable and highly rewarding endeavor this book will be useful to physicists, mathematicians, and computer scientists who look at random graph models in which point locations affect the shape and properties of the resulting network: physicists will acquaint themselves with complex networks having rich modeling capabilities (e.g. models for random interaction particle systems such as spin glasses), mathematicians may discover connections of the networks with formal systems (much like the connection of the classical ErdsRényi random graph properties with first- and second-order logic), and computer scientists will greatly appreciate the applicability of the theory given in the book to the study of realistic, ad hoc mobile networks in which network node connections change rapidly and unpredictably as a function of the geometry of the current node positions.' Yannis Stamatiou, Mathematical Reviews

Muu info

The first rigorous introduction for graduate students and scientists to techniques and problems motivated by wireless data networks.
Preface ix
List of notation
xi
Introduction
1(16)
Discrete network models
3(3)
The random tree
3(2)
The random grid
5(1)
Continuum network models
6(8)
Poisson processes
6(4)
Nearest neighbour networks
10(1)
Poisson random connection networks
11(1)
Boolean model networks
12(1)
Interference limited networks
13(1)
Information-theoretic networks
14(1)
Historical notes and further reading
15(2)
Phase transitions in infinite networks
17(52)
The random tree; infinite growth
17(4)
The random grid; discrete percolation
21(8)
Dependencies
29(2)
Nearest neighbours; continuum percolation
31(6)
Random connection model
37(11)
Boolean model
48(3)
Interference limited networks
51(15)
Mapping on a square lattice
56(2)
Percolation on the square lattice
58(4)
Percolation of the interference model
62(1)
Bound on the percolation region
63(3)
Historical notes and further reading
66(3)
Connectivity of finite networks
69(31)
Preliminaries: modes of convergence and Poisson approximation
69(2)
The random grid
71(6)
Almost connectivity
71(1)
Full connectivity
72(5)
Boolean model
77(11)
Almost connectivity
78(3)
Full connectivity
81(7)
Nearest neighbours; full connectivity
88(4)
Critical node lifetimes
92(6)
A central limit theorem
98(1)
Historical notes and further reading
98(2)
More on phase transitions
100(21)
Preliminaries: Harris-FKG Inequality
100(1)
Uniqueness of the infinite cluster
101(6)
Cluster size distribution and crossing paths
107(7)
Threshold behaviour of fixed size networks
114(5)
Historical notes and further reading
119(2)
Information flow in random networks
121(36)
Information-theoretic preliminaries
121(10)
Channel capacity
122(2)
Additive Gaussian channel
124(3)
Communication with continuous time signals
127(2)
Information-theoretic random networks
129(2)
Scaling limits; single source-destination pair
131(5)
Multiple source-destination pairs; lower bound
136(10)
The highway
138(1)
Capacity of the highway
139(3)
Routing protocol
142(4)
Multiple source-destination pairs; information-theoretic upper bounds
146(9)
Exponential attenuation case
148(3)
Power law attenuation case
151(4)
Historical notes and further reading
155(2)
Navigation in random networks
157(28)
Highway discovery
157(2)
Discrete short-range percolation (large worlds)
159(2)
Discrete long-range percolation (small worlds)
161(10)
Chemical distance, diameter, and navigation length
162(5)
More on navigation length
167(4)
Continuum long-range percolation (small worlds)
171(10)
The role of scale invariance in networks
181(1)
Historical notes and further reading
182(3)
Appendix
185(5)
A.1 Landau's order notation
185(1)
A.2 Stirling's formula
185(1)
A.3 Ergodicity and the ergodic theorem
185(2)
A.4 Deviations from the mean
187(1)
A.5 The Cauchy-Schwartz inequality
188(1)
A.6 The singular value decomposition
189(1)
References 190(4)
Index 194


Massimo Franceschetti is assistant professor of electrical engineering at the University of California, San Diego. His work in communication system theory sits at the interface between networks, information theory, and electromagnetic wave propagation. Ronald Meester is professor of mathematics at the Vrije Universiteit Amsterdam. He has published broadly in percolation theory, spatial random processes, self-organized criticality, ergodic theory, and forensic statistics and is the author of Continuum Percolation (with Rahul Roy) and A Natural Introduction to Probability Theory.