Almost mixing of all orders and CLT for some $\mathbb{Z}^d$-actions on subgroups of $\mathbb{F}\_p^{\mathbb{Z}^d}$

Guy Cohen; Jean-Pierre Conze

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arXiv · 1609.06484

Almost mixing of all orders and CLT for some $\mathbb{Z}^d$-actions on subgroups of $\mathbb{F}\_p^{\mathbb{Z}^d}$

Guy Cohen·Jean-Pierre Conze

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Abstract

For N d-actions by algebraic endomorphisms on compact abelian groups, the existence of non-mixing configurations is related to "S-unit type" equations and plays a role in limit theorems for such actions. We consider a family of endomorphisms on shift-invariant subgroups of F Z d p and show that there are few solutions of the corresponding equations. This implies the validity of the Central Limit Theorem for different methods of summation.

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Guy Cohen, Jean-Pierre Conze. 2016-09-21. Almost mixing of all orders and CLT for some $\mathbb{Z}^d$-actions on subgroups of $\mathbb{F}\_p^{\mathbb{Z}^d}$. https://arxiv.org/abs/1609.06484

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