2021/01/25 by Pierre Perruchaud, Perruchaud, Pierre
Biochemistry, Genetics and Molecular Biology · Mathematics · #60B20 (Primary) 60G53 #60J60 (Secondary) #Diffusion and Search Dynamics #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.2101.10426
openalex publication_date 2021/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.