Colloquium on January 26, 2009

Alexander Hartmann
Universität Oldenburg

Simulation of rare events

Monte Carlo simulations with biased sampling techniques are used to study the distribution of very rare objects (p=10^(-40)) in different statistical mechanics systems.
As examples, three different models are considered here.

A. Sequence alignment is a method to compare Protein sequences. The distribution of alignment scores over random sequences is studied in the biologically relevent region of high scores. Significant deviation from the Gumbel distribution are found, which is used so far in molecular biology databases.

B. Random graphs are the basis for many models in statistical mechanics. Here the distribution of the number of clusters is obtained numerically and compared with new analytical calculations.

C. The Potts model is one of the prototypical models for phase transitions. It is shown how the partition function for large systems can be calculated very accurately by studying the distribution of clusters in the Fortuin-Kasteleyn representation.