The main theme of these lecture notes is to analyze heat conduction on disordered media
such as fractals and percolation clusters by means of both probabilistic and analytic …

These notes cover one of the topics programmed for the St Petersburg School in Probability
and Statistical Physics of June 2012. The aim is to review recent mathematical …

We study biased random walk on subcritical and supercritical Galton–Watson trees
conditioned to survive in the transient, sub-ballistic regime. By considering offspring laws …

We consider the Bouchaud trap model on the integers in the case that the trap distribution
has a slowly varying tail at infinity. Our main result is a functional limit theorem for the model …

Let T be a rooted supercritical multi-type Galton-Watson (MGW) tree with types coming from
a finite alphabet, conditioned to non-extinction. The λ-biased random walk (X_t)_t\ge0 on T …

We study biased random walk on the infinite connected component of supercritical
percolation on the integer lattice Z d for d≥ 2. For this model, Fribergh and Hammond …

We prove CLTs for biased randomly trapped random walks in one dimension. By
considering a sequence of regeneration times, we will establish an annealed invariance …

We consider the quenched localisation of the Bouchaud trap model on the positive integers
in the case that the trap distribution has a slowly varying tail at infinity. Our main result is that …

In this paper we consider the one-dimensional, biased, randomly trapped random walk with
infinite-variance trapping times. We prove sufficient conditions for the suitably scaled walk to …

We consider the Bouchaud trap model on the integers in the case that the trap distribution
has a slowly varying tail at infinity. We prove that the model eventually localises on exactly …