{"paper":{"title":"Quenched Central Limit Theorems for Random Walks in Random Scenery","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Julien Poisat, Nadine Guillotin-Plantard (ICJ)","submitted_at":"2012-10-23T06:09:47Z","abstract_excerpt":"Random walks in random scenery are processes defined by $$Z_n:=\\sum_{k=1}^n\\omega_{S_k}$$ where $S:=(S_k,k\\ge 0)$ is a random walk evolving in $\\mathbb{Z}^d$ and $\\omega:=(\\omega_x, x\\in{\\mathbb Z}^d)$ is a sequence of i.i.d. real random variables. Under suitable assumptions on the random walk $S$ and the random scenery $\\omega$, almost surely with respect to $\\omega$, the correctly renormalized sequence $(Z_n)_{n\\geq 1}$ is proved to converge in distribution to a centered Gaussian law with explicit variance."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6135","kind":"arxiv","version":1},"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"}