Lectures and Colloquia during the semester

**January 14, 2002**

Humboldt-Universität zu Berlin

Rudower Chaussee 5

12489 Berlin

Room 4.101
- map -

** Lecture - 14.00 Uhr c.t.**

### Jeff Kahn - Rutgers University, NJ

### Random independent sets

Uniform and more general "hard-core" distributions on the collection
of independent sets of a large graph are of interest in their own
right (in statistical physics as well as combinatorics), and have also
found some combinatorial uses. We will discuss some questions,
results and connections involving such distributions. Possible
key words and phrases: phase transition, chromatic index, entropy,
Dedekind's Problem.

** Colloquium - 16 Uhr s.t.**

### Manuel Bodirsky - Humboldt-Universität zu Berlin

### Algorithms for period problems and applications to the analysis of Markov chains

*Abstract:*
Stable state distributions play an important role for the theory
of Markov chains, since they are related with long-run properties
of probabilistic systems. However, there are Markov chains where
the probability to be in a certain set of states converges, but the
Markov chain has no stable state distribution.

In this talk I present how to reduce convergence problems on non-
ergodic Marcov chains to equivalent combinatorial period problems,
and show how number theory helps to solve these problems.

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