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

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.