Article

Probability Theory and Related Fields

, Volume 157, Issue 1, pp 453-507

First online:

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

  • D. A. CroydonAffiliated withDepartment of Statistics, University of Warwick Email author 
  • , A. FriberghAffiliated withCIMS, New York University
  • , T. KumagaiAffiliated withRIMS, Kyoto University

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.

Mathematics Subject Classification

Primary 60K37 Secondary 60F17 60G70 60J80