Term 1, 2009/10

Lecturer: Stefan Grosskinsky

Lectures: Wed 11-12 in MS.04, Thu 10-11 in B3.02 and Fri 12-1 in MS.05

Classes: Fri 3-4 in D1.13

• Revision class Mon 19.04. at 2pm in D1.13
  
• Fri 13.11., no lecture from 12-1, 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 non-probabilistic 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