On the annealed large deviation rate function for a multi-dimensional random walk in random environment

We derive properties of the rate function in Varadhan’s (annealed) large deviation principle for multidimensional, ballistic random walk in random environment, in a certain neighborhood of the zero set of the rate function. Our approach relates the LDP to that of regeneration times and distances. The analysis of the latter is possible due to the i.i.d. structure of regenerations. 1 Introduction and Statement of Main Results This paper studies annealed large deviations for multidimensional random walks in random envi-ronments (RWRE), in the ballistic regime. We will be concerned with nearest neighbor RWRE with uniformly elliptic i.i.d. environments, modeled as follows. Let Ed: = {x ∈ Zd: ‖x ‖ = 1