3 papers
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-ph2024
Quantum Mechanics of Arc-Sine and Semi-Circle Distributions: A Unified Approach
Luigi Accardi, Tarek Hamdi, Yun Gang Lu
This paper continues the program of applying beyond physics the technique of \textbf{probabilistic quantization} and extending to the quantum mechanics associated with the arc--sin…