We study the discrete massless Gaussian free field on Zd, d≥2, in the presence of a disordered square-well potential supported on a finite strip around zero. The disorder is introduced by reward/penalty interaction coefficients, which are given by i.i.d. random variables. Under minimal...

We consider a nearest neighbor random walk on Z which is reflecting at 0 and perturbed when it reaches its maximum. We compute the law of the hitting times and derive many corollaries, especially invariance principles with (rather) explicit descriptions of the asymptotic laws. We also obtain...

Consider a centred random walk in dimension one with a positive finite variance σ2, and let τB be the hitting time for a bounded Borel set B with a non-empty interior. We prove the asymptotic Px(τBn)∼2/πσ−1VB(x)n−1/2 and provide an explicit formula for the limit VB as a function of...

We give a complete classification of scaling limits of randomly trapped random walks and associated clock processes on Zd, d≥2. Namely, under the hypothesis that the discrete skeleton of the randomly trapped random walk has a slowly varying return probability, we show that the scaling limit of...

A subcritical branching process in random environment (BPRE) is considered whose associated random walk does not satisfy the Cramer condition. The asymptotics for the survival probability of the process is investigated, and a Yaglom type conditional limit theorem is proved for the number of...

General characterizations of ergodic Markov chains have been developed in considerable detail. In this paper, we study the transience for discrete-time Markov chains on general state spaces, including the geometric transience and algebraic transience. Criteria are presented through bounding the...

We compute the second order correction for the cover time of the binary tree of depth n by (continuous-time) random walk, and show that with probability approaching 1 as n increases, τcov=|E|[2log2⋅n−logn/2log2+O((loglogn)8)], thus showing that the second order correction differs from the...

We prove a law of large numbers for a class of Zd-valued random walks in dynamic random environments, including non-elliptic examples. We assume for the random environment a mixing property called conditional cone-mixing and that the random walk tends to stay inside wide enough space–time...