Velocity surface disorder of large deviation rate functions of the random walk in strongly mixing environment

TL;DR

This paper proves large deviation principles for random walks in strongly mixing environments, showing the shape of the rate functions and their behavior under controlled disorder, with illustrative examples.

Contribution

It establishes the existence and properties of large deviation rate functions for random walks in strongly mixing environments, including their shape and conforming behavior.

Findings

Rate functions have the same zero set, either a point or a line segment.

Under controlled disorder, quenched and annealed rate functions conform on compact sets.

Illustrative example provided by F. Rassoul-Agha.

Abstract

In this work, we establish the existence of large deviation principles of random walk in strongly mixing environments. The quenched and annealed rate functions have 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. Whenever the level of disorder is controlled, the two rate functions are shown to conform on compact sets at the boundary and in the interior both under strongly mixing conditions.