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 and we will cover some of this material.

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


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

Similar courses elsewhere

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


Lecture times: MWF 1.00 - 2.00pm room 330 EVANS

Office Hours Thursdays 2.15 - 3.45 in 351 Evans

If you email me ( put "STAT 206" in subject line.

Requirements for students. Students taking the course for credit need to do one of the following.

Class-by-class schedule

This will mostly be a debriefing of what I have done, rather than a plan for the future......