{"paper":{"title":"CLT for random walks of commuting endomorphisms on compact abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Guy Cohen, Jean-Pierre Conze","submitted_at":"2014-11-13T13:39:00Z","abstract_excerpt":"Let $\\Cal S$ be an abelian group of automorphisms of a probability space $(X, {\\Cal A}, \\mu)$ with a finite system of generators $(A_1, ..., A_d)$. Let $A^{\\el}$ denote $A_1^{\\ell_1} ...                                                                                                                                                                            \nA_d^{\\ell_d}$, for ${\\el}= (\\ell_1, ..., \\ell_d)$. If $(Z_k)$ is a random walk on $\\Z^d$, one can study the asymptotic distribution of the sums $\\sum_{k=0}^{n-1} \\, f \\circ A^{\\,{Z_k(\\omega)}}$\nand $\\sum_{\\el \\in \\Z^d} \\PP(Z_n= \\el) \\, A^\\el"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3540","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"}