Random Networks for Communication: From Statistical Physics to Information Systems
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.
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Phase transitions in infinite networks
Connectivity of finite networks
More on phase transitions
Information flow in random networks
Navigation in random networks
The role of scale invariance in networks
Historical notes and further reading
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achievable rate annulus attenuation function bond percolation boolean model box Bn branching process centred codeword communication compute connection function consider constant construction converges converges in distribution critical crossing paths decentralised algorithm define denote density dual graph dual lattice edges ergodic exists expected number Figure finite follows geometric Hence highway implies independent inequality infinite cluster infinite component infinite connected component inside Bn inside the box isolated nodes least Lemma logm logn long-range connections nearest neighbour nodes noise Note Notice number of points obtain parameter partition percolation process phase transition plane points inside Poisson distribution Poisson point process Poisson process Poisson random variable proof of Theorem random connection model random graph random grid random network realisation rectangle result scale sequence shortcut side length signal site percolation square lattice subsquares supercritical target tends to zero transmit union bound upper bound vertex vertices