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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…
math.PR2025
Spectral distribution of the free Jacobi process with equal rank projections
Nizar Demni, Tarek Hamdi
The free Jacobi process is the radial part of the compression of the free unitary Brownian motion by two free orthogonal projections in a non commutative probability space. In this…
math.PR2024
Moments of the free Jacobi process: a matrix approach
Nizar Demni, Tarek Hamdi
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 algorit…