Abstract:
In a range of models of random walks in random environments, the asymptotic behaviour of the walk is driven by a trapping mechanism arising due to the walk being slowed in adverse regions in the environment. Random walks on trees are a natural example as dead-ends in the tree form traps which slow the walk. In this talk, we discuss biased random walks on both supercritical and subcritical Galton-Watson trees conditioned to survive. In particular, we describe how the trapping observed in these models is influenced by the structure of the tree and focus on questions concerning properties of the limiting speed, the scale of the fluctuations and the issues concerning quenched and functional results.
Biography:
Dr. Bowditch did his undergraduate degree and Ph.D. at the University of Warwick. Following this, he stayed at Warwick for six months as an Early Career Fellow before moving to Singapore where he is a Research Fellow at NUS.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai