{"paper":{"title":"Deviations of a random walk in a random scenery with stretched exponential tails","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Nina Gantert, Remco van der Hofstad, Wolfgang K\\\"onig","submitted_at":"2004-11-16T10:43:52Z","abstract_excerpt":"Let (Z_n)_{n\\in\\N_0} be a d-dimensional random walk in random scenery, i.e., Z_n=\\sum_{k=0}^{n-1}Y_{S_k} with (S_k)_{k\\in\\N_0} a random walk in Z^d and (Y_z)_{z\\in Z^d} an i.i.d. scenery, independent of the walk.\n  We assume that the random variables Y_z have a stretched exponential tail. In particular, they do not possess exponential moments. We identify the speed and the rate of the logarithmic decay of Pr(Z_n>t_n n) for all sequences (t_n)_{n\\in\\N} satisfying a certain lower bound. This complements previous results, where it was assumed that Y_z has exponential moments of all orders. In con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0411361","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}