Nizar Demni

GENERATING FUNCTIONS OF CAUCHY–STIELTJES TYPE FOR ORTHOGONAL POLYNOMIALS

We characterize by the use of free probability the family of measures for which the mulitiplicative renormalization method applies with

The Laguerre process and generalized Hartman–Watson law

h(x) = (1-x)^_{-1}

Radial Dunkl Processes Associated with Dihedral Systems

. This provides a representation formula for their Voiculescu Transforms.

First Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes

In this paper, we study complex Wishart processes or the so-called Laguerre processes

Generalized Bessel function of Type D

(X_t)_{t\geq0}

Analysis of generalized Poisson distributions associated with higher Landau levels

. We are interested in the behaviour of the eigenvalue process; we derive some useful stochastic differential equations and compute both the infinitesimal generator and the semi-group. We also give absolute-continuity relations between different indices. Finally, we compute the density function of the so-called generalized Hartman--Watson law as well as the law of

Spectral Distribution of the Free Unitary Brownian Motion: Another Approach

T_0:=\inf\{t,\det(X_t)=0\}

Product formula for Jacobi polynomials, spherical harmonics and generalized Bessel function of dihedral type

when the size of the matrix is 2.

FREE MARTINGALE POLYNOMIALS FOR STATIONARY JACOBI PROCESSES

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 polynomials. Then, a skew product decomposition, involving only independent Bessel processes, is given and the tail distribution of the first hitting time of boundary of the Weyl chamber is computed.

Generalized Stieltjes Transforms of Compactly-Supported Probability Distributions: Further Examples ?

We provide two equivalent approaches for computing the tail distribution of the first hitting time of the boundary of the Weyl chamber by a radial Dunkl process. The first approach is based on a spectral problem with initial value. The second one expresses the tail distribution by means of the