15 citations · 37 across the 19 of their papers we have counts for
21 papers
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…
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…
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…
Open Quantum Random Walks and Quantum Markov chains on Trees II: The recurrence
Farrukh Mukhamedov, Abdessatar Souissi, Tarek Hamdi +1
In the present paper, we construct QMC (Quantum Markov Chains) associated with Open Quantum Random Walks such that the transition operator of the chain is defined by OQRW and the r…
Open Quantum Random Walks and Quantum Markov chains on Trees I: Phase transitions
Farrukh Mukhamedov, Abdessatar Souissi, Tarek Hamdi
In the present paper, we construct QMC (Quantum Markov Chains) associated with Open Quantum Random Walks such that the transition operator of the chain is defined by OQRW and the r…
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 quantum mechanics canonically associated to free probability Part I: Free momentum and associated kinetic energy
Luigi Accardi, Tarek Hamdi, Yun Gang Lu
After a short review of the quantum mechanics canonically associated with a classical real valued random variable with all moments, we begin to study the quantum mechanics canonica…
Quantum Markov Chains on the Comb graphs: Ising model
Farrukh Mukhamedov, Abdessatar Souissi, Tarek Hamdi
In the present paper, we construct quantum Markov chains (QMC) over the Comb graphs. As an application of this construction, it is proved the existence of the disordered phase for…
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…
Support of the Brown measure of the product of a free unitary Brownian motion by a free self-adjoint projection
Nizar Demni, Tarek Hamdi
The first part of this paper is devoted to the Brown measure of the product of the free unitary Brownian motion by an arbitrary free non negative operator. Our approach follows the…
On star-Moments of the compression of the free unitary Brownian motion by a free projection
Nizar Demni, Tarek Hamdi
In this paper, we derive explicit expressions for the moments and for the mixed moments of the compression of a free unitary Brownian motion by a free projection. While the moments…
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…
Spectral distribution of large-size Brownian motions on the complex linear group
Nizar Demni, Tarek Hamdi
We show how the approach used in `N. Demni, T. Hmidi. Spectral Distribution of the Free unitary Brownian motion: another approach. Sem. Probab. XLIV. 2012. 191-206.' applies to des…
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…