{"paper":{"title":"Limit theorems for one and two-dimensional random walks in random scenery","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fabienne Castell (LATP), Fran\\c{c}oise P\\`ene (LM), Nadine Guillotin--Plantard (ICJ)","submitted_at":"2011-03-23T06:15:33Z","abstract_excerpt":"Random walks in random scenery are processes defined by $Z_n:=\\sum_{k=1}^n\\xi_{X_1+...+X_k}$, where $(X_k,k\\ge 1)$ and $(\\xi_y,y\\in{\\mathbb Z}^d)$ are two independent sequences of i.i.d. random variables with values in ${\\mathbb Z}^d$ and $\\mathbb R$ respectively. We suppose that the distributions of $X_1$ and $\\xi_0$ belong to the normal basin of attraction of stable distribution of index $\\alpha\\in(0,2]$ and $\\beta\\in(0,2]$. When $d=1$ and $\\alpha\\ne 1$, a functional limit theorem has been established in \\cite{KestenSpitzer} and a local limit theorem in \\cite{BFFN}. In this paper, we establi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4453","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"}