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

Understand

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.