FMIE (Finite Markov Information Exchange) Processes

This is a cover page for a summer 2012 mini-course to be given at Warwick in June and at Cornell in July. It will be a compressed and slightly updated version of a course given in Berkeley in Spring 2011 -- slides from that course available here.

These are the slides prepared for Warwick (though I didn't show them all, in the first 3 lectures).
Lecture 1: Overview
Lecture 2: The Averaging Process
Lecture 3: The Voter Model
Lecture 4: Pandemic and its variants

These were expanded slightly for the Cornell lectures.
Lecture 1: Overview
Lecture 2: The Averaging Process
Lecture 3: The Voter Model
Lecture 4: The Pandemic Process
Lecture 5: Some analogs of epidemics, and some research suggestions
Lecture 6: And now for something completely different

Draft write-up

Here is a 29 page draft write-up of this material. But unlike typical lecture - paper combinations, there is less material in the paper than in the lectures.

Relevant completed papers of mine:

Advance reading

We draw on ideas from two well-developed fields, so it will be helpful to have some familiarity with them.

1. Finite reversible Markov chains. This topic is treated in much more detail in Levin-Peres-Wilmer Markov Chains and Mixing Times and in Aldous-Fill Reversible Markov Chains and Random Walks on Graphs. The most relevant topics are 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. See Chapters 4, 5, 10, 12 of Levin-Peres-Wilmer.

2. Interacting particle systems. Chapter 10 (and then 6) of Grimmett's Probability on Graphs provide the gentlest introduction. Durrett's 1988 monograph Lecture notes on particle systems and percolation provides more sophisticated intuition, if you can find a copy.

Also browse the unorganized list of possibly relevant papers (from the 2011 course) to get a feeling for the breadth of disciplines where FMIE processes have been studied.