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arXiv · 2009.04762

Infinite p-adic random matrices and ergodic decomposition of p-adic Hua measures

Theodoros Assiotis
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Abstract

Neretin constructed an analogue of the Hua measures on the infinite $p$-adic matrices $Mat\left(\mathbb{N},\mathbb{Q}_p\right)$. Bufetov and Qiu classified the ergodic measures on $Mat\left(\mathbb{N},\mathbb{Q}_p\right)$ that are invariant under the natural action of $GL(\infty,\mathbb{Z}_p)\times GL(\infty,\mathbb{Z}_p)$. In this paper we solve the problem of ergodic decomposition for the $p$-adic Hua measures introduced by Neretin. We prove that the probability measure governing the ergodic decomposition has an explicit expression which identifies it with a Hall-Littlewood measure on partitions. Our arguments involve certain Markov chains.

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Theodoros Assiotis. 2021-07-27. Infinite p-adic random matrices and ergodic decomposition of p-adic Hua measures. https://arxiv.org/abs/2009.04762

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