Almost mixing of all orders and CLT for some $\mathbb{Z}^d$-actions on subgroups of $\mathbb{F}_p^{\mathbb{Z}^d}$ - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2016

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

Résumé

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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Dates et versions

hal-01369614 , version 1 (21-09-2016)

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Citer

Guy Cohen, Jean-Pierre Conze. Almost mixing of all orders and CLT for some $\mathbb{Z}^d$-actions on subgroups of $\mathbb{F}_p^{\mathbb{Z}^d}$. 2016. ⟨hal-01369614⟩
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