Random walks in random environments and their diffusion analogues have been a source
of surprising phenomena and challenging problems, especially in the non-reversible …

The present volume contains the most advanced theories on the martingale approach to
central limit theorems. Using the time symmetry properties of the Markov processes, the …

We consider the simple random walk on the (unique) infinite cluster of super-critical bond
percolation in ℤ d with d≥ 2. We prove that, for almost every percolation configuration, the …

We introduce an exactly-solvable model of random walk in random environment that we call
the Beta RWRE. This is a random walk in ZZ which performs nearest neighbour jumps with …

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 …

We consider the motion of a particle under a continuum random environment whose
distribution is given by the Howitt-Warren flow. In the moderate deviation regime, we …

We study a continuous-time random walk, X, on ℤ d in an environment of dynamic random
conductances taking values in (0,∞). We assume that the law of the conductances is ergodic …

The first-passage time for a single diffusing particle has been studied extensively, but the
first-passage time of a system of many diffusing particles, as is often the case in physical …

In this paper we study a random walk in a one-dimensional dynamic random environment
consisting of a collection of independent particles performing simple symmetric random …

In many-particle diffusions, particles that move the furthest and fastest can play an outsized
role in physical phenomena. A theoretical understanding of the behavior of such extreme …