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arXiv · 2610.00134

Markov chains arising in the study of random matrices over pro-finite rings

Nikita Lvov
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Abstract

Recent work of the author investigates certain random processes, valued in abelian p-groups, that naturally arise in the study of Haar random matrices over $\mathbb{Z}_p$. It was found, somewhat surprisingly, that these processes are reversible Markov chains. In this short note, we give a simple alternative derivation of this fact. The new derivation also proves that this phenomenon is not specific to $\mathbb{Z}_p$, but generalizes to Haar random matrices over any profinite local ring.

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Nikita Lvov. 2026-09-09. Markov chains arising in the study of random matrices over pro-finite rings. https://arxiv.org/abs/2610.00134

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