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arXiv · 1605.09600

Ergodic measures on spaces of infinite matrices over non-Archimedean locally compact fields

Alexander I. Bufetov·Yanqi Qiu
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Abstract

Let $F$ be a non-discrete non-Archimedean locally compact field and $\mathcal{O}_F$ the ring of integers in $F$. The main results of this paper are Theorem 1.2 that classifies ergodic probability measures on the space $\mathrm{Mat}(\mathbb{N}, F)$ of infinite matrices with enties in $F$ with respect to the natural action of the group $\mathrm{GL}(\infty,\mathcal{O}_F) \times \mathrm{GL}(\infty,\mathcal{O}_F)$ and Theorem 1.6 that, for non-dyadic $F$, classifies ergodic probability measures on the space $\mathrm{Sym}(\mathbb{N}, F)$ of infinite symmetric matrices with respect to the natural action of the group $\mathrm{GL}(\infty,\mathcal{O}_F)$.

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Alexander I. Bufetov, Yanqi Qiu. 2016-05-31. Ergodic measures on spaces of infinite matrices over non-Archimedean locally compact fields. https://doi.org/10.1112/s0010437x17007412

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