Diffusivity and Ballistic Behavior of Random Walk in Random Environment

Abstract

In this thesis, we study the diffusive and ballistic behaviors of random walk in random environment (RWRE) in an integer lattice with dimension at least 2. Our contributions are in three directions: a conditional law of large numbers and regeneration structures for RWRE in Gibbsian environments, quenched invariance principles for balanced elliptic (but non uniformly elliptic) environments, and a proof of the Einstein relation for balanced iid uniformly elliptic environments.

PhD thesis

References in corpus (2)

• Shortest spanning trees and a counterexample for random walks in random environments
• Effective Polynomial Ballisticity Condition for Random Walk in Random Environment