Günter Last (KIT)

Stochastic analysis of the Dirichlet process

Abstract tba.

Jan 26

2:30-
6:00 pm

at RUB

Vitali Wachtel (Bielefeld)
Berry-Esseen inequality for random walks conditioned to stay positive

Patricia Alonso Ruiz (Jena)
An isoperimetric inequality for (fractal) spaces with different micro- and macrostructure

David Criens (Freiburg)
Stochastic control problems with irregular coefficients and $L_d$-drift

Dec 15

Panagiotis Spanos (University of Bochum)

Percolation on transitive graphs of polynomial growth.

In this talk, we will discuss a special model of percolation, called spread-out percolation. Specifically, let $G$ be a vertex-transitive graph equipped with the graph metric, and let $r>0$ be a range parameter. We define $G_r$ to be the graph with the same vertex set as $G$, where two vertices are connected by an edge whenever their distance in $G$ is at most $r$. The spread-out percolation on $G$ with degree parameter $\lambda$ and range $r$ is the Bernoulli percolation on $G_r$ in which each edge is retained with probability $\lambda / \deg(G_r)$. We prove that for graphs of superlinear polynomial growth,
$$
p_c = \frac{1+o(1)}{\deg(G_r)}
\quad\text{as } r\to\infty,
$$
that is, the critical degree parameter for the existence of an infinite cluster tends to $1$ as $r$ grows. This theorem generalises a result of Penrose for $\mathbb{Z}^d$. The model was introduced by Hara and Slade in the study of mean-field behaviour. We will present open problems as well as new results in the area. Based on joint work with M. Tointon.

Oct 27

2:30-
6:00 pm

at RUB

Helene Götz (Dortmund)
Large deviations for spectral measures of random matrices under nonstandard scaling

Philipp Tuchel (Bochum)
Asymptotic behavior of random projections of high-dimensional $\ell_p^N$ balls

Roman Gambelin (Essen)
An extension of the algebraic Aldous diffusion