Abstract
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 and only if d=2. In the large scale and large time limit, we show that Λ converges to the usual (Markovian) Dyson Brownian motion under suitable normalisation, regardless of the dimension.
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