2016/06/13 by Yanqi Qiu, Qiu, Yanqi
Computer Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Graph theory and applications #Probability (math.PR) #Representation Theory (math.RT) #Topological and Geometric Data Analysis #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1606.03959
openalex publication_date 2016/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let O(∞) and U(∞) be the inductively compact infinite orthogonal group and infinite unitary group respectively. The classifications of ergodic probability measures with respect to the natural group action of O(∞)× O(m) on Mat(ℕ× m, ℝ) and that of U(∞)× U(m) on Mat(ℕ× m, ℂ) are due to Olshanski. The original proofs for these results are based on the asymptotic representation theory. In this note, by applying the Vershik-Kerov method, we propose a simple method for obtaining these two classifications, making it accessible to pure probabilists.