论文标题
P-Adic HUA措施的无限P-ADIC随机矩阵和厄乳
Infinite p-adic random matrices and ergodic decomposition of p-adic Hua measures
论文作者
论文摘要
NERETIN在无限$ P $ -ADIC矩阵$ MAT \ left（\ Mathbb {n}，\ Mathbb {q} _p \ right）$上构建了HUA量度的类似物。 bufetov和Qiu对$ at \ left（\ mathbb {n}，\ mathbb {q} _p \ right）$进行了分类，这些度量是在$ gl（\ infty，\ infty，\ mathbb {z} _p {z} _p Times gl fime gl（_p imp fimes gl）（\ math）下，它们是不变的，它们是不变的。在本文中，我们解决了Neretin引入的$ p $ -Adic HUA措施的千古分解问题。我们证明，控制沿子的分解的概率度量具有明确的表达式，可以通过分区上的霍尔小木测量标识它。我们的论点涉及某些马尔可夫连锁店。
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.
