Kinetic Dyson Brownian motion
Kinetic Dyson Brownian motion
We study the spectrum of the kinetic Brownian motion in the space of d×d Hermitian matrices, d≥2. We show that the eigenvalues stay distinct for all times, and that the process Λ of eigenvalues is a kinetic diffusion (i.e. the pair (Λ,Λ˙) of Λ and its derivative is Markovian) if …