2014/10/05 by Yanqi Qiu, Qiu, Yanqi
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.1410.1167
openalex publication_date 2014/10/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The ergodic decomposition of a family of Hua-Pickrell measures on the space of infinite Hermitian matrices is studied. Firstly, we show that the ergodic components of Hua-Pickrell probability measures have no Gaussian factors, this extends a result of Alexei Borodin and Grigori Olshanski. Secondly, we show that the sequence of asymptotic eigenvalues of Hua-Pickrell random matrices is balanced in certain sense and has a "principal value" coincides with the γ1 parameter of ergodic components. This allow us to complete the program of Borodin and Olshanski on the description of the ergodic decomposition of Hua-Pickrell probability measures. Finally, we extend the aforesaid results to the case of infinite Hua-Pickrell measues. By using the theory of σ-finite infinite determinantal measures recently introduced by A. I. Bufetov, we are able to identify the ergodic decomposition of Hua-Pickrell infinite measures to some explicit σ-finite determinantal measures on the space of point configurations in ℝ^*. The paper resolves a problem of Borodin and Olshanski.