Random walks as well as diffusions in random media are considered. Methods are developed that allow one to establish large deviation results for both the 'quenched' and the 'averaged' case.

We consider a system of interacting diffusions. The variables are to be thought of as charges at sites indexed by a periodic one-dimensional lattice. The diffusion preserves the total charge and the… (More)

A strong maximal principle for the operator (a/st) + L, is a statement of the form: "for each open 1 c [0, oo) x Rd and each (to, x0) e 9 there is a set Y(to, x0) 91 with the property that (af/lt) +… (More)

We study the homogenization of some Hamilton-Jacobi-Bellman equations with a vanishing second-order term in a stationary ergodic random medium under the hyperbolic scaling of time and space. Imposing… (More)

space of graphs contd. I Suppose that t(H,Gn) tends to a limit t(H) for every H. I Then Lovász & Szegedy proved that there is a natural “limit object” in the form of a function f ∈ W, where W is the… (More)

The world we live in has never been very predictable, and randomness has always been part of our lives. There is ample evidence that our ancestors did enjoy playing games of chance, and the early… (More)

A classical theorem of Sanov identiies the entropy function as the rate functional for the large deviations of the empirical measure. sequence of independent and identically distributed random… (More)

This paper is based on Wald Lectures given at the annual meeting of the IMS in Minneapolis during August 2005. It is a survey of the theory of large deviations. 1. Large deviations for sums. The role… (More)

In 1956, Dobrushin proved an important central limit theorem for nonhomogeneous Markov chains. In this note, a shorter and different proof elucidating more the assumptions is given through martingale… (More)