, Volume 157, Issue 1-2, pp 453-507,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 26 Oct 2012

Biased random walk on critical Galton–Watson trees conditioned to survive

Abstract

We consider the biased random walk on a critical Galton–Watson tree conditioned to survive, and confirm that this model with trapping belongs to the same universality class as certain one-dimensional trapping models with slowly-varying tails. Indeed, in each of these two settings, we establish closely-related functional limit theorems involving an extremal process and also demonstrate extremal aging occurs.