Biased random walk on critical Galton-Watson trees conditioned to   survive
  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. 
David A. Croydon, Alexander Fribergh and Takashi Kumagai
math.PR