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math.PR2026
Second moments associated with finite free multiplicative convolution
Nicolas Gilliers, Andrea Pettenello
We compute the second mixed moment of elementary symmetric polynomials in the eigenvalues of the random matrix model , where and are positive, and is a Haar-dis…
math.PR2025
Finite free probability and transforms of Jacobi processes
Nizar Demni, Nicolas Gilliers, Tarek Hamdi
In this paper, we study the transforms of Jacobi processes in the frameworks of free and finite free probability theories. We begin by deriving a partial differential equation…