Moments of the free Jacobi process: a matrix approach

2024/04/17 by Nizar Demni, Demni, Nizar, Tarek Hamdi +1 · 1 citation
Mathematics · Physics and Astronomy · #15B52 #33C80 #46L54 #60B20 #Combinatorics (math.CO) #FOS: Mathematics #Operator Algebras (math.OA) #Probability (math.PR) #Quantum chaos and dynamical systems #Random Matrices and Applications #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2404.11708

openalex publication_date 2024/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the large size limit of the moment formula derived in \citeDHS 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 Lemma 3 in \citeBia. 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 ₄F₃ functions taken at unity.

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