Lectures and Colloquia during the semester

**November 29, 2004**

Humboldt-Universität zu Berlin

Rudower Chaussee 25

12489 Berlin

Humboldt-Kabinett, 1st floor, between house III and IV
- map -

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

### Svante Janson -Uppsala University

### Asymptotics for generalized Polya urns

*Abstract:*
Consider a generalized Polya urn, which contains balls of different
colours and which evolves by drawing a ball at random and then adding a
set of balls depending on the drawn colour.

We study the asymptotic composition of the urn. In the irreducible case,
the result depends crucially on the ratio between the two largest (real
parts of) eigenvalues of a matrix describing the additions; if this
ratio is at most 1/2, the asymptotic distribution is normal, but not
otherwise. In reducible cases there are further possibilities, including
stable and Mittag-Leffler limits.

Some applications to random trees will be included.

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

### Dirk Schlatter -Humboldt-Universität zu Berlin

### Spanning subgraphs of random graphs

*Abstract:*
I will present a theorem of Riordan about spanning subgraphs in the
uniform random graph model *G(n,m)*. While trying to avoid most of
the technical details, I will sketch the main ideas and steps in
the proof, and show an application: the threshold for the spanning
d-dimensional cube.

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