{"paper":{"title":"Stable limit laws for random walk in a sparse random environment I: moderate sparsity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Iksanov, Alexander Marynych, Alexander Roitershtein, Dariusz Buraczewski, Piotr Dyszewski","submitted_at":"2018-04-27T18:17:16Z","abstract_excerpt":"A random walk in a sparse random environment is a model introduced by Matzavinos et al. [Electron. J. Probab. 21, paper no. 72: 2016] as a generalization of both a simple symmetric random walk and a classical random walk in a random environment. A random walk $(X_n)_{n\\in \\mathbb{N}\\cup\\{0\\}}$ in a sparse random environment $(S_k,\\lambda_k)_{k\\in\\mathbb{Z}}$ is a nearest neighbor random walk on $\\mathbb{Z}$ that jumps to the left or to the right with probability $1/2$ from every point of $\\mathbb{Z}\\setminus \\{\\ldots,S_{-1},S_0=0,S_1,\\ldots\\}$ and jumps to the right (left) with the random prob"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10633","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"}