Browsing by Author "Mörters, Pete"
Now showing 1 - 1 of 1
Results Per Page
Sort Options
- ItemModerate deviations for random walk in random scenery(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Fleischmann, Klaus; Mörters, Pete; Wachtel, VitaliWe investigate random walks in independent, identically distributed random sceneries under the assumption that the scenery variables satisfy Cramér's condition. We prove moderate deviation principles in dimensions d ≥ 2, covering all those regimes where rate and speed do not depend on the actual distribution of the scenery. In the case d ≥ 4 we even obtain precise asymptotics for the annealed probability of a moderate deviation, extending a classical central limit theorem of Kesten and Spitzer. In d ≥ 3, an important ingredient in the proofs are new concentration inequalities for self-intersection local times of random walks, which are of independent interest, whilst in $ = 2 we use a recent moderate deviation result for self-intersection local times, which is due to Bass, Chen and Rosen.