Moments of the free Jacobi process: a matrix approach
Abstract
We compute the large size limit of the moment formula derived in 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 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 1-balanced 4F3 functions taken at unity.
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