MA4H3 Interacting Stochastic Processes
Term 1, 2009/10
Lecturer: Stefan Grosskinsky
Lectures: Wed 1112 in MS.04, Thu 1011 in B3.02 and Fri 121 in MS.05
Classes: Fri 34 in D1.13
 Revision class Mon 19.04. at 2pm in D1.13
 Fri 13.11., no lecture from 121, due to conference Kotecky60 (which is related to the course material). Class at 4pm takes place in D1.07!
This module provides an introduction to basic stochastic models of collective phenomena arising from the interactions of a large number of identical components. It aims towards a qualitative and quantitative understanding of possible phase transitions using minimal models that capture the main features. Examples from physics, biology and social sciences, such as spread of epidemics/opinions, traffic flow, crystal surface growth or population dynamics provide motivations and illustrate the results. The second main aspect of the course is a proper mathematical description of these models as stochastic processes with spatial interactions, and an introduction to basic probabilistic tools for their analysis.
It is an advanced module on stochastic processes continuing e.g. MA3G9  Probability and Discrete Mathematics or ST333  Applied Stochastic Processes. These have related content but are not necessary prerequisites, MA4H3 is accessible to anyone with basic knowledge in probability/Markov processes. If you are particularly interested in biological applications also the following modules can be interesting, MA4E7  Population Dynamics: Ecology and Epidemiology and MA390  Topics in Mathematical Biology, which mainly use nonprobabilistic approaches.
Materials
 Third example sheet: ips_10_sheet3.pdf (full version)
 Second example sheet: ips_10_sheet2.pdf
 First example sheet: ips_10_sheet1.pdf

Final version of the course notes: notes_ips_10.pdf (12.12.09)
NOTE! Prop. 4.15 changed, extra conditions had to be added.
 A copy of the course description: MA4H3_09.pdf
 An introduction to Markov chains is given in the first chapter of the course notes for CO905  Stochastic processes: notes_co905.pdf
 Last year's webpage
Suggested Literature
 T.M. Liggett: Stochastic Interacting Systems, Springer (1999)

H. Spohn: Large Scale Dynamics of Interacting Particles, Springer (1991)

T.M. Liggett: Interacting Particle Systems  An Introduction, ICTP Lecture Notes 17 (2004), http://publications.ictp.it/lns/vol17/vol17toc.html

L. Bertini et al: Stochastic interacting particle systems out of equilibrium, J. Stat. Mech. (2007) P07014, http://arxiv.org/abs/0705.1247