Biased random walks on subcritical Galton-Watson trees

Date
2015/10/30 Fri 15:30 - 17:00
Room
3号館552号室
Speaker
Adam Bowditch
Affiliation
University of Warwick
Abstract

In this talk, I will discuss biased random walks on subcritical Galton-Watson trees conditioned to survive; in particular, the time taken for the walk to traverse the backbone, that is, the collection of vertices with an infinite line of descent. Due to trapping phenomena in the random environment, there are five main escape regimes that the walk may follow depending only on the bias and the offspring distribution. I will explain how each of these regimes arises, noting how changes in certain parameters influences the limiting behaviour. I will then outline the general ideas behind all of them, sketch a proof of one case and draw comparisons with walks on critical and supercritical trees conditioned to survive.