29 citations · 104 across the 60 of their papers we have counts for
44 papers · 1 filter
Brownian motion on the complex general group and the non-compact Jacobi process
Martin Auer, Nizar Demni, Nicolas Gilliers
In this paper, we introduce and study a new non Hermitian matrix-valued process built from truncations of Brownian motion on complex positive-definite matrices and of its inverse.…
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…
Brownian motion and stochastic areas on complex full flag manifolds
Fabrice Baudoin, Nizar Demni, Teije Kuijper +1
We show that the Brownian motion on the complex full flag manifold can be represented by a matrix-valued diffusion obtained from the unitary Brownian motion. This representation ac…
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…
Stochastic areas, Horizontal Brownian Motions, and Hypoelliptic Heat Kernels
Fabrice Baudoin, Nizar Demni, Jing Wang
The monograph is devoted to the study of stochastic area functionals of Brownian motions and of the associated heat kernels on Lie groups and Riemannian manifolds. It is essentiall…