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Moments of the free Jacobi process: A matrix approach

Part of: Combinatorics, graph theory, probability theory, statistics Special matrices Selfadjoint operator algebras Probability theory on algebraic and topological structures

Published online by Cambridge University Press:  10 March 2025

Nizar Demni  and
Tarek Hamdi Open the ORCID record for Tarek Hamdi [Opens in a new window]
Nizar Demni
Affiliation:
Department of Mathematics, New York University in Abu Dhabi, Saadiyat Island, P.O. Box 129188, Abu Dhabi, UAE e-mail: nd2889@nyu.edu
Tarek Hamdi*
Affiliation:
Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah, Saudi Arabia and Laboratoire d’Analyse Mathématiques et applications LR11ES11, Université de Tunis El-Manar, Tunis, Tunisia
*
e-mail: t.hamdi@qu.edu.sa
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Abstract

We compute the large size limit of the moment formula derived in [14] for the Hermitian Jacobi process at fixed time. Our computations rely on the polynomial division algorithm which allows to obtain cancellations similar to those obtained in [3, Lemma 3]. In particular, we identify the terms contributing to the limit and show they satisfy a double recurrence relation. We also determine explicitly some of them and revisit a special case relying on Carlitz summation identity for terminating $1$-balanced ${}_4F_3$ functions taken at unity.

Keywords

Hermitian Jacobi processfree Jacobi processMethod of momentshypergeometric functionsCarlitz summation formula

MSC classification

Primary: 15B52: Random matrices 33C80: Connections with groups and algebras, and related topics 46L54: Free probability and free operator algebras 60B20: Random matrices (probabilistic aspects; for algebraic aspects see ) 97K60: Distributions and stochastic processes

Information

Type
Article
Information
Canadian Mathematical Bulletin , Volume 68 , Issue 3 , September 2025 , pp. 966 - 991
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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