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

2020/09/10 by Assiotis, Theodoros
#Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2009.04762

Abstract

Neretin constructed an analogue of the Hua measures on the infinite p-adic matrices Mat(ℕ,ℚ_p). Bufetov and Qiu classified the ergodic measures on Mat(ℕ,ℚ_p) that are invariant under the natural action of GL(∞,ℤ_p)× GL(∞,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.

Related

• Infinite Random Matrices and Ergodic decomposition of Finite or Infinite Hua-Pickrell measures
• Ergodic measures on infinite skew-symmetric matrices over non-Archimedean local fields
• Ergodic measures and infinite matrices of finite rank
• Random permutations and unique fully supported ergodicity for the Euler adic transformation
• Ergodic Properties of the Random Walk Adic Transformation over the Beta Transformation