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

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.

Minor revision according to referee reports. To appear Transactions of AMS

References in corpus (2)

• Infinite random matrices and ergodic measures
• Ergodic Decomposition for Inverse Wishart Measures on Infinite Positive-Definite Matrices

Cited by in corpus (1)

• Limits and fluctuations of $p$-adic random matrix products