Central limit theorem for Z d + - actions by toral endomorphisms
نویسنده
چکیده
In this paper we prove the central limit theorem for the following multisequence N1 ∑ n1=1 ... Nd ∑ nd=1 f(A1 1 ...A nd d x) where f is a Hölder’s continue function, A1, ..., Ad are s× s partially hyperbolic commuting integer matrices, and x is a uniformly distributed random variable in [0, 1]. Then we prove the functional central limit theorem, and the almost sure central limit theorem. The main tool is the S-unit theorem.
منابع مشابه
Central Limit Theorem for Commutative Semigroups of Toral Endomorphisms
Abstract. Let S be an abelian finitely generated semigroup of endomorphisms of a probability space (Ω,A, μ), with (T1, ..., Td) a system of generators in S. Given an increasing sequence of domains (Dn) ⊂ N, a question is the convergence in distribution of the normalized sequence |Dn| 12 ∑ k∈Dn f ◦ T , or normalized sequences of iterates of barycenters Pf = ∑ j pjf ◦ Tj, where T k = T k1 1 ...T ...
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