Velocity surface disorder of large deviation rates for high-dimensional random walk in strongly mixing environment

Abstract

In this work, we establish the large deviation principles of random walk in strongly mixing environments. We show that the quenched and annealed rate functions share the same zero-set whose shape is either a singleton point or a line segment, with an illustrative example communicated and given by F. Rassoul-Agha. Furthermore, this paper reveals that under sufficiently low disorder, the two rate functions match on compact sets of both the interior and the boundary of the domain under finitely strongly mixing condition.

arXiv commentTo appear on Electronic Journal of Probability