Information recovery from randomly mixed-up message text.
Integrability of exit times and ballisticity for random walks in Dirichlet environment.
Internal DLA in a random environment
Invariance principle for Mott variable range hopping and other walks on point processes
We consider a random walk on a homogeneous Poisson point process with energy marks. The jump rates decay exponentially in the -power of the jump length and depend on the energy marks via a Boltzmann-like factor. The case corresponds to the phonon-induced Mott variable range hopping in disordered solids in the regime of strong Anderson localization. We prove that for almost every realization of the marked process, the diffusively rescaled random walk, with an arbitrary start point, converges to...
Invariance principle for the random conductance model with dynamic bounded conductances
We study a continuous time random walk in an environment of dynamic random conductances in . We assume that the conductances are stationary ergodic, uniformly bounded and bounded away from zero and polynomially mixing in space and time. We prove a quenched invariance principle for , and obtain Green’s functions bounds and a local limit theorem. We also discuss a connection to stochastic interface models.