## 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.