{"paper":{"title":"Central limit theorem for commutative semigroups of toral endomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Guy Cohen, Jean-Pierre Conze (IRMAR)","submitted_at":"2013-04-16T19:04:25Z","abstract_excerpt":"Let $\\Cal S$ be an abelian finitely generated semigroup of endomorphisms of a probability space $(\\Omega, {\\Cal A}, \\mu)$, with $(T_1, ..., T_d)$ a system of generators in ${\\Cal S}$. Given an increasing sequence of domains $(D_n) \\subset \\N^d$, a question is the convergence in distribution of the normalized sequence $|D_n|^{-\\frac12} \\sum_{{\\k} \\, \\in D_n} \\, f \\circ T^{\\,{\\k}}$, for $f \\in L^2_0(\\mu)$, where $T^{\\k}= T_1^{k_1} ... T_d^{k_d}$, ${\\k}= (k_1, ..., k_d) \\in {\\N}^d$. After a preliminary spectral study when the action of $\\Cal S$ has a Lebesgue spectrum, we consider $\\N^d$- or $\\Z^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4556","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"}