Large deviations in the reinforced random walk model on trees

Large Deviations for Random Walk in Random

Large Deviations for Random Trees.

We consider large random trees under Gibbs distributions and prove a Large Deviation Principle (LDP) for the distribution of degrees of vertices of the tree. The LDP rate function is given explicitly. An immediate consequence is a Law of Large Numbers for the distribution of vertex degrees in a large random tree. Our motivation for this study comes from the analysis of RNA secondary structures.

Averaged Large Deviations for Random Walk in a Random Environment

Abstract. In his 2003 paper, Varadhan proves the averaged large deviation principle (LDP) for the mean velocity of a particle performing random walk in a random environment (RWRE) on Z with d ≥ 1, and gives a variational formula for the corresponding rate function Ia. Under the non-nestling assumption (resp. Kalikow’s condition), we show that Ia is strictly convex and analytic on a non-empty op...

Large Deviations for Random Walk in a Random Environment

In this work, we study the large deviation properties of random walk in a random environment on Z with d ≥ 1. We start with the quenched case, take the point of view of the particle, and prove the large deviation principle (LDP) for the pair empirical measure of the environment Markov chain. By an appropriate contraction, we deduce the quenched LDP for the mean velocity of the particle and obta...

Quenched Large Deviations for Random Walk in a Random Environment

We take the point of view of a particle performing random walk with bounded jumps on Z in a stationary and ergodic random environment. We prove the quenched large deviation principle (LDP) for the pair empirical measure of the environment Markov chain. By an appropriate contraction, we deduce the quenched LDP for the mean velocity of the particle and obtain a variational formula for the corresp...