Introduction to mathematical physics, spring 2011
Stochastic particle systems
Stochastic particle systems (or "Interacting particle systems") are stochastic processes that are widely
used in physics (in non-equilibrium statistical mechanics) and in biology (spatial population dynamics).
In the simplest case (the simple exclusion process) particles perform random jumps on a lattice with
the constraint that no site contains more than one particle. The course provides an introduction to the
mathematical theory of these processes and then discusses in more detail the simple exclusion process
where recently some remarkable connections to combinatorics and random matrices have been obtained.
Review of probability
Markov jump processes and their generators
Particle systems: simple exclusion process (SEP), zero range process
One dimensional SEP: random matrices, KPZ equation, universality
Weeks 4-9 and 11-18 tuesday 14-16, thursday 14-16 C123.
Easter holiday 21.-27.4.
First lecture: Thursday January 27!!
No lectures on Tuesday April 5 and Thursday April 7!!
Next lecture: Thursday April 28!!
The exam is on thursday the 11th of August at 10-14.
Timo Seppäläinen: Translation Invariant Exclusion Processes http://www.math.wisc.edu/~seppalai/excl-book/ajo.pdf
T. M. Liggett: Interacting particle systems, volume 276 of Grundlehren der Mathematischen Wissenschaften, Springer- Verlag, New York, 1985
H. Spohn. Large scale dynamics of interacting particles. Springer-Verlag, Berlin, 1991
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