NEWS

Spatial Networks

## STAT C206A (= MATH C223A) Fall 2013: David Aldous

STAT 206, with catalog description Advanced Topics in Probability and Stochastic Processes, is intended to have a different subject each semester. My subject is

## Spatial Networks

This is a broad and diffuse topic which has been studied in many disciplines, but the course will emphasize stochastic aspects.
1. We start with an overview in this 100-page survey by Marc Barthelemy, which examines models and data from a statistical physics viewpoint and shows some interesting real data. The survey does not emphasize math theorems, but I will use it as a starting point for discussing what is known mathematics and what are possible math research problems.
2. We then segue into more specific technical work, from the list of possibly-relevant papers.
3. There is no systematic definition-theorem-proof account of our central topic, general random spatial networks, but the books below treat related topics such as
• Stochastic geometry
• The random geometric graph, continuum percolation and their use in models of wireless communication
• Algorithmic aspects of spatial network construction
and we will cover some of this material.

For the record I will maintain a list of networks that are mentioned in the course.

### Books

There are no books with precisely the focus of this course. The most closely related, as regards math topics, are
1. Baccelli - Blaszczyszyn (2009): Stochastic Geometry and Wireless Networks: Volume I Theory.
2. Franceschetti - Meester (2007): Random networks for communication: from statistical physics to information systems.
3. Narasimhan - Smid (2007): Geometric spanner networks.
4. Penrose (2003): Random geometric graphs.
5. Preparata - Shamos (1993): Computational Geometry: An Introduction.
6. Steele (1997): Probability theory and combinatorial optimization.
7. Stoyan - Kendall - Mecke (1995): Stochastic geometry and its applications.
(2,3,4,7 are on reserve in the Math-Stat library). For a broad-ranging overview of quantitative aspects of networks, without specialized math, by far the best book is
For a textbook on some basic math see
• Newman (2010): Networks: An Introduction.

### Similar courses elsewhere

These are courses with useful info online. Mostly with less mathematical emphasis.