So it's a two-level modeling framework. The bottom level is the "geometry", specified by the rate matrix (\nu_{ij}), of how agents meet. The top level is the "content" of whatever phenomenon we are trying to model.

Existing literature tends to focus on specific geometries,
building up from simple to more
complex interaction rules.
A future research focus would be to attempt a more thorough analysis of
simple interaction rules used with general geometries,
analogous to the standard theory of finite Markov chains.
Much of the present course will
involve looking at existing literature which might be meaningfully translated
into the FMIE context. In particular one can
take algorithmic questions, interpretable as concerning ``spread of information",
which have been studied
in the traditional *n*-vertex graph context, and reconsider them in the
FMIE context.

- [A] Lectures 1 - 2. Overview: FMIE processes.
- [B] Lectures 2 - 5. Finite reversible Markov chains, emphasising mixing and hitting times, and the standard examples of random walks on the complete graph, the d-dimensional grid, and on random graphs with prescribed degree distributions. This topic is treated in much more detail in Markov Chains and Mixing Times and in Reversible Markov Chains and Random Walks on Graphs.
- [C] Lectures 5 - 7. Averaging model.
- [D] Lectures 7 - 8. Voter model.
- [E] Lectures 9 - 13. Epidemic models and first-passage percolation.
- Subsequent lectures are written more hastily ..............
- [F] Lectures 14 - 15. SIR and SIS epidemics, contact process.
- [G] Lectures 16 - 18. Kinetic Ising; averaging with some fixed opinions; Fashionista.
- [H] Lectures 19 - 20. Axelrod model from Castellano (2000). PD on lattice as cellular automaton, from Nowak-May (1993); on real networks from Holme (2003). Naming Game, from Baronchelli (2006).
- 4/11: Elchanan Mossel will talk about his work Reaching Consensus on Social Networks.
- 4/13: Brian Skyrms will talk on "learning in signalling games".
- 4/18
**No Class.**

**Wednesday 20 April**

- Christopher Lin: the Chierichetti - Lattanzi - Panconesi paper Rumour spreading and graph conductance.
- Douglas Rizzolo : the Chatterjee-Durrett paper Asymptotic Behavior of Aldous' Gossip Process.

**Monday 25 April**

- Jack Reilly: More about the rank-based game. (course project).
- Miki Racz: Combining voter and exclusion dynamics.
- Anupam Prakash: COMPUTING SYMMETRIC FUNCTIONS ON MEMORY BOUNDED SOCIAL NETWORKS.

**Wednesday 27 April**

- Osman Akgun: the Karrer - Newman paper A message passing approach for general epidemic models.
- Dan Lanoue: Worst-case behavior of FMIEs. (course project).

**Wednesday 4 May**

- Joe Austerweil: FMIE analysis of memory.
- Noan Forman: Role of Forgetting in Evolution and Learning of Language.

- M. O. Jackson, Social and Economic Networks (2008) and David Easley and Jon Kleinberg Networks, Crowds, and Markets (2010) provide the best "big picture", but do not engage graduate-level mathematical probability.
- Rick Durrett, Random Graph Dynamics (2006) and Mark Newman, Networks: An Introduction (2010) focus on models of network formation.
- Moez Draief and Laurent Massoulie, Epidemics and Rumours in Complex Networks, (2010).
- A. Barrat, M. Barthelemy, and A. Vespignani, Dynamical Processes on Complex Networks, (2008).

(Kleinberg; Cornell)
The Structure of Information Networks

(Leskovec; Stanford)
Social and
Information Network Analysis

(Saberi; Stanford)
Information Networks

(Kearns; U. Penn)
Social networks and algorithmic game theory

More advanced and specialized than the above is

(Mossel; Berkeley)
Social Choice and Networks.

Our course does **not** focus on models of network formation, which is a major topic
of other courses; see e.g.
my old course
Random graphs and complex networks.

**Office Hours:** Mondays 12.30 - 2.30 in 351 Evans.

If you email me (aldous@stat) put "STAT 260" in subject line.

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

- Read a recent paper and give a 20-minute talk during last 2 weeks of semester.
- Do one of the projects which will be mentioned in class (and then listed here). These range from theory (proving something) to simulations to "literature search" (what is known relevant to some vague question?).