Directed random walk on an oriented percolation cluster
Vortrag von Prof. Dr. Matthias Birkner
Sprecher eingeladen von: Prof. Dr. Erwin Bolthausen
Datum: 06.11.13 Zeit: 17.15 - 18.15 Raum: ETH
We consider a directed random walk on the backbone of the infinite cluster generated by supercritical oriented percolation, and exhibit suitable regeneration structures to obtain a law of large numbers and a quenched central limit theorem. The walk can be interpreted as the space-time embedding of the ancestral lineage of a sampled individual in the stationary discrete-time contact process. Extensions to more general population models, leading to random walks in correlated space-time environments, and also to several walkers are of interest in population genetic applications. I will discuss approaches to extend the results in this direction. Based on joint work, in part in progress, with Jiri Cerny, Andrej Depperschmidt and Nina Gantert.