Random Networks for Communication From Statistical Physics to Information Systems 1st Edition by Massimo Franceschetti, Ronald Meester 0511378556 9780521854429

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Product details:

ISBN 10: 0511378556 

ISBN 13: 9780521854429

Author: Massimo Franceschetti, Ronald Meester

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.

Table of contents:

1 Introduction

1.1 Discrete network models

1.1.1 The random tree

1.1.2 The random grid

1.2 Continuum network models

1.2.1 Poisson processes

1.2.2 Nearest neighbour networks

1.2.3 Poisson random connection networks

1.2.4 Boolean model networks

1.2.5 Interference limited networks

1.3 Information-theoretic networks

1.4 Historical notes and further reading

Exercises

2 Phase transitions in infinite networks

2.1 The random tree; infinite growth

2.2 The random grid; discrete percolation

2.3 Dependencies

2.4 Nearest neighbours; continuum percolation

2.5 Random connection model

2.6 Boolean model

2.7 Interference limited networks

2.7.1 Mapping on a square lattice

2.7.2 Percolation on the square lattice

2.7.3 Percolation of the interference model

2.7.4 Bound on the percolation region

2.8 Historical notes and further reading

Exercises

3 Connectivity of finite networks

3.1 Preliminaries: modes of convergence and Poisson approximation

3.2 The random grid

3.2.1 Almost connectivity

3.2.2 Full connectivity

3.3 Boolean model

3.3.1 Almost connectivity

3.3.2 Full connectivity

3.4 Nearest neighbours; full connectivity

3.5 Critical node lifetimes

3.6 A central limit theorem

3.7 Historical notes and further reading

Exercises

4 More on phase transitions

4.1 Preliminaries: Harris–FKG Inequality

4.2 Uniqueness of the infinite cluster

4.3 Cluster size distribution and crossing paths

4.4 Threshold behaviour of fixed size networks

4.5 Historical notes and further reading

Exercises

5 Information flow in random networks

5.1 Information-theoretic preliminaries

5.1.1 Channel capacity

5.1.2 Additive Gaussian channel

5.1.3 Communication with continuous time signals

5.1.4 Information-theoretic random networks

5.2 Scaling limits; single source–destination pair

5.3 Multiple source–destination pairs; lower bound

5.3.1 The highway

5.3.2 Capacity of the highway

5.3.3 Routing protocol

5.4 Multiple source–destination pairs; information-theoretic upper bounds

5.4.1 Exponential attenuation case

5.4.2 Power law attenuation case

5.5 Historical notes and further reading

Exercises

6 Navigation in random networks

6.1 Highway discovery

6.2 Discrete short-range percolation (large worlds)

6.3 Discrete long-range percolation (small worlds)

6.3.1 Chemical distance, diameter, and navigation length

6.3.2 More on navigation length

6.4 Continuum long-range percolation (small worlds)

6.5 The role of scale invariance in networks

6.6 Historical notes and further reading

Exercises

Appendix

A.1 Landau’s order notation

A.2 Stirling’s formula

A.3 Ergodicity and the ergodic theorem

A.4 Deviations from the mean

A.4.1 Markov’s inequality

A.4.2 Chebyshev’s inequality

A.4.3 Chernoff’s bounds for a Poisson random variable

A.5 The Cauchy–Schwarz inequality

A.6 The singular value decomposition

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Tags: Massimo Franceschetti, Ronald Meester, Random, Communication