15 citations · 37 across the 19 of their papers we have counts for
13 papers · 1 filter
Finite free probability and transforms of Jacobi processes
Nizar Demni, Nicolas Gilliers, Tarek Hamdi
We calculate the averaged characteristic polynomial and its finite transform for the Hermitian Jacobi process at any fixed time . We give a direct proof that this sequence…
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…
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…
Summing free unitary Brownian motions with applications to quantum information
Nizar Demni, Tarek Hamdi
Motivated by quantum information theory, we introduce a dynamical random state built out of the sum of independent unitary Brownian motions. In the large size limit, its…
Relating moments of self-adjoint polynomials in two orthogonal projections
Nizar Demni, Tarek Hamdi
Given two orthogonal projections in a non commutative tracial probability space, we prove relations between the moments of , of and of and…
The Hermitian Jacobi process: simplified formula for the moments and application to optical fibers MIMO channels
Nizar Demni, Tarek Hamdi, Abdessatar Souissi
Using a change of basis in the algebra of symmetric functions, we compute the moments of the Hermitian Jacobi process. After a careful arrangement of the terms and the evaluation o…
Schur-Weyl duality and the Product of randomly-rotated symmetries by a unitary Brownian motion
Nizar Demni, Tarek Hamdi
In this paper, we introduce and study a unitary matrix-valued process which is closely related to the Hermitian matrix-Jacobi process. It is precisely defined as the product of a d…
Spectral distribution of the free Jacobi process, revisited
Tarek Hamdi
We obtain a description for the spectral distribution of the free Jacobi process for any initial pair of projections. This result relies on a study of the unitary operator $RU_tSU_…
Free mutual information for two projections
Tarek Hamdi
The present paper provides a proof of for two projections without any extra assumptions. An an…
Liberation, free mutual information and orbital free entropy
Tarek Hamdi
We present here some connections between the liberation process for projections and its counterpart for symmetries when the…
Inverse of the flow and moments of the free Jacobi process associated with a single projection
Nizar Demni, Tarek Hamdi
This paper is a companion to a series of papers devoted to the study of the spectral distribution of the free Jacobi process associated with a single projection. Actually, we notic…
Monotone and boolean unitary Brownian motions
Tarek Hamdi
The additive monotone (resp. boolean) unitary Brownian motion is a non-commutative stochastic process with monotone (resp. boolean) independent and stationary increments which are…
Stochastic analysis for obtuse random walks
Uwe Franz, Tarek Hamdi
We present a construction of the basic operators of stochastic analysis (gradient and divergence) for a class of discrete-time normal martingales called obtuse random walks. The ap…