Alessandra Faggionato

Large deviations of the empirical flow for continuous time Markov chains

We consider a continuous time Markov chain on a countable state space and prove a joint large deviation principle for the empirical measure and the empirical flow, which accounts for the total number of jumps between pairs of states. We give a direct proof using tilting and an indirect one by contraction from the empirical process.

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 A-power of the jump length and depend on the energy marks via a Boltzmann--like factor. The case A=1 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 arbitrary start point, converges to a Brownian motion whose diffusion matrix is positive definite, and independent of the environment. Finally, we extend the above result to other point processes including diluted lattices.

Diffusivity in one-dimensional generalized Mott variable-range hopping models

We consider random walks in random environment which are generalized versions of well known effective models for Mott variable--range hopping. We study the homogenized diffusion constant of the random walk in the one--dimensional case. We prove various estimates on the the low--temperature behavior which confirm and extend previous work by physicists.

Isoperimetric inequalities and mixing time for a random walk on a random point process

We consider the random walk on a simple point process on

Large deviation principles for nongradient weakly asymmetric stochastic lattice gases

\Bbb{R}^d

Random walks on quasi one dimensional lattices: Large deviations and fluctuation theorems

,

The influence of dimension on the relaxation process of East-like models : rigorous results

d\geq2

Level 2.5 Large Deviations for Continuous-Time Markov Chains with Time Periodic Rates

, whose jump rates decay exponentially in the

Mixing length scales of low temperature spin plaquettes models

\alpha

Discrete Kinetic Models for Molecular Motors: Asymptotic Velocity and Gaussian Fluctuations

-power of jump length. The case