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  1. Article

    Correction: Relating moments of self-adjoint polynomials in two orthogonal projections

    Nizar Demni, Tarek Hamdi in Advances in Operator Theory (2024)

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    Article

    Summing free unitary Brownian motions with applications to quantum information

    Motivated by quantum information theory, we introduce a dynamical random density matrix built out of the sum of \(k \ge 2\) ...

    Tarek Hamdi, Nizar Demni in Letters in Mathematical Physics (2023)

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    Article

    Relating moments of self-adjoint polynomials in two orthogonal projections

    Given two orthogonal projections \(\{P,Q\}\) { P ...

    Nizar Demni, Tarek Hamdi in Advances in Operator Theory (2022)

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    Article

    Quaternionic Brownian Windings

    We define and study the three-dimensional windings along Brownian paths in the quaternionic Euclidean, projective and hyperbolic spaces. In particular, the asymptotic laws of these windings are shown to be Gau...

    Fabrice Baudoin, Nizar Demni, **g Wang in Journal of Theoretical Probability (2021)

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    Article

    The Horizontal Heat Kernel on the Quaternionic Anti-De Sitter Spaces and Related Twistor Spaces

    The geometry of the quaternionic anti-de Sitter fibration is studied in details. As a consequence, we obtain formulas for the horizontal Laplacian and subelliptic heat kernel of the fibration. The heat kernel ...

    Fabrice Baudoin, Nizar Demni, **g Wang in Potential Analysis (2020)

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    Article

    Markov Semi-groups Associated with the Complex Unimodular Group \(Sl(2,{\mathbb {C}})\)

    In this paper, we derive the explicit expressions of the Markov semi-groups constructed by Biane (ESAIM Probab Stat 15:S2–S10, 2011) from the restriction of a particular positive definite function on the complex ...

    Nizar Demni in Journal of Fourier Analysis and Applications (2019)

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    Article

    Integral representation of the sub-elliptic heat kernel on the complex anti-de Sitter fibration

    We derive an integral representation for the subelliptic heat kernel of the complex anti-de Sitter fibration. Our proof is different from the one used in Wang (Potential Anal 45:635–653, 2016) since it appeals...

    Fabrice Baudoin, Nizar Demni in Archiv der Mathematik (2018)

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    Article

    Moments of the Hermitian Matrix Jacobi Process

    In this paper, we compute the expectation of traces of powers of the Hermitian matrix Jacobi process for a large enough but fixed size. To proceed, we first derive the semi-group density of its eigenvalues pro...

    Luc Deleaval, Nizar Demni in Journal of Theoretical Probability (2018)

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    Chapter

    Large Deviations for Clocks of Self-similar Processes

    The Lamperti correspondence gives a prominent role to two random time changes: the exponential functional of a Lévy process drifting to $$\in...

    Nizar Demni, Alain Rouault, Marguerite Zani in In Memoriam Marc Yor - Séminaire de Probab… (2015)

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    Chapter

    Spectral Distribution of the Free Unitary Brownian Motion: Another Approach

    We revisit the description provided by Ph. Biane of the spectral measure of the free unitary Brownian motion. We actually construct for any $...

    Nizar Demni, Taoufik Hmidi in Séminaire de Probabilités XLIV (2012)

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    Chapter

    Radial Dunkl Processes Associated with Dihedral Systems

    We are interested in radial Dunkl processes associated with dihedral systems. We write down the semi-group density and as a by-product the generalized Bessel function and the W-invariant generalized Hermite polyn...

    Nizar Demni in Séminaire de Probabilités XLII (2009)