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Infinite \(p\)-adic random matrices and ergodic decomposition of \(p\)-adic Hua measures. (English) Zbl 1491.60007

Y. A. Neretin [Izv. Math. 77, No. 5, 941–953 (2013; Zbl 1284.22013); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 77, No. 5, 95–10 (2013)] has constructed Hua measures on the set of infinite \(p\)-adic matrices. A. I. Bufetov and Y. Qiu [Compos. Math. 153, No. 12, 2482–2533 (2017; Zbl 1386.37004)] described the measures on the same space that are ergodic with respect to a certain natural action. In this paper, the author gives explicit ergodic decomposition of Neretin’s Hua measures.

MSC:

60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
60B20 Random matrices (probabilistic aspects)
37A35 Entropy and other invariants, isomorphism, classification in ergodic theory

Keywords:

Hua measures
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References:

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