确定性系统中的多维局部极限定理及其在多项式多重平均不收敛中的应用

Zemer Kosloff, Shrey Sanadhya
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引用次数: 0

摘要

我们证明,对于每个遍历和非周期性概率保全系统$(X,\mathcal{B},m,T)$,存在$f:X\to \mathbb{Z}^d$,其相应的循环满足 d 维局部中心极限定理。我们利用二维结果来解决黄、邵和叶以及弗兰齐基纳基斯和霍斯特关于非交换零熵变换的多项式多重平均的不收敛问题。
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Multidimensional local limit theorem in deterministic systems and an application to non-convergence of polynomial multiple averages
We show that for every ergodic and aperiodic probability preserving system $(X,\mathcal{B},m,T)$, there exists $f:X\to \mathbb{Z}^d$, whose corresponding cocycle satisfies the d-dimensional local central limit theorem. We use the 2-dimensional result to resolve a question of Huang, Shao and Ye and Franzikinakis and Host regarding non-convergence of polynomial multiple averages of non-commuting zero entropy transformations.
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