MOMENTS OF THE FREE JACOBI PROCESS: A MATRIX APPROACH

Nizar Demni; Tarek Hamdi

doi:10.4153/S0008439525000244

MOMENTS OF THE FREE JACOBI PROCESS: A MATRIX APPROACH

Nizar Demni, Tarek Hamdi

Mathematics

Research output: Contribution to journal › Article › peer-review

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 Lemma 3 in [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 ₄F₃functions taken at unity.

Original language	English (US)
Journal	Canadian Mathematical Bulletin
DOIs	https://doi.org/10.4153/S0008439525000244
State	Accepted/In press - 2025

Keywords

Carlitz summation formula
complete ordinary Bell polynomial
free Jacobi process
generalized Chu-Vandermonde identity
Hermitian Jacobi process
hypergeometric functions
Method of moments

ASJC Scopus subject areas

General Mathematics

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10.4153/S0008439525000244

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title = "MOMENTS OF THE FREE JACOBI PROCESS: A MATRIX APPROACH",

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 Lemma 3 in [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 4F3functions taken at unity.",

keywords = "Carlitz summation formula, complete ordinary Bell polynomial, free Jacobi process, generalized Chu-Vandermonde identity, Hermitian Jacobi process, hypergeometric functions, Method of moments",

author = "Nizar Demni and Tarek Hamdi",

year = "2025",

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language = "English (US)",

journal = "Canadian Mathematical Bulletin",

issn = "0008-4395",

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AU - Hamdi, Tarek

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N2 - 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 Lemma 3 in [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 4F3functions taken at unity.

AB - 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 Lemma 3 in [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 4F3functions taken at unity.

KW - Carlitz summation formula

KW - complete ordinary Bell polynomial

KW - free Jacobi process

KW - generalized Chu-Vandermonde identity

KW - Hermitian Jacobi process

KW - hypergeometric functions

KW - Method of moments

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JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

ER -

MOMENTS OF THE FREE JACOBI PROCESS: A MATRIX APPROACH

Abstract

Keywords

ASJC Scopus subject areas

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