May 9, 2014
Location: Achter de Dom 22 (Utrecht), room 001
Exit distributions for random walks in random environments
We report about recent results on random walks in anisotropic random environments which were obtained with Erich Baur. This refines and extends results which were previously obtained with Ofer Zeitouni. We also discuss ongoing research with Ofer Zeitouni on exit laws for two-dimensional RWREs where the disorder is only marginally contracting.
Routing on trees
We consider three different schemes for signal routing on a tree. The vertices of the tree represent transceivers that can transmit and receive signals, and are equipped with i.i.d. weights representing the strength of the transceivers. Also the edges of the tree are equipped with i.i.d. weights, representing the costs for passing the edges. For each one of our schemes, we derive sharp conditions on the distributions of the vertex weights and the edge weights that determine when a signal transmitted by the root can reach infinitely far. The proof techniques include multi-type branching processes and branching random walks. Joint work with Nina Gantert.