Moments of the free Jacobi process: a matrix approach
Probability
2025-09-10 v2 Combinatorics
Operator Algebras
Abstract
We compute the large size limit of the moment formula derived in \cite{DHS} 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 \cite{Bia}. 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 -balanced functions taken at unity.
Keywords
Cite
@article{arxiv.2404.11708,
title = {Moments of the free Jacobi process: a matrix approach},
author = {Nizar Demni and Tarek Hamdi},
journal= {arXiv preprint arXiv:2404.11708},
year = {2025}
}