Biased random walks on random paths and critical random trees
Vortrag von Dr. David Croydon
Datum: 24.04.13 Zeit: 17.15 - 19.00 Raum: Y27H25
In this talk, I will discuss two problems that are motivated by understanding how biased random walks behave on large critical percolation clusters. Firstly, I will describe how introducing a bias slows down random walks on critical Galton-Watson branching process trees (this is joint work with Alexander Fribergh, New York University, and Takashi Kumagai, Kyoto University). Secondly, I consider the biased random walk on the range of a random walk. In this setting, I indicate how a localization result can be proved by adapting techniques originally developed for one-dimensional random walks in random environments in Sinai's regime. In both settings, it is possible to make a precise statement about how the increasing the strength of the bias affects the long-time behaviour of the associated random walk.