2004/02/29 by Makoto Katori, Hideki Tanemura · 5 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Bayesian Methods and Mixture Models #Random Matrices and Applications #cond-mat.stat-mech #math-ph #math.MP #math.PR
paper · pdf · doi:10.1063/1.1765215
published as J. Math. Phys. 45 (2004) 3058-3085 · LaTeX, 27 pages, 4 figures, v3: Minor corrections made for publication in J. Math. Phys
arxiv created 2004/06/15 · openalex publication_date 2004/07/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
As an extension of the theory of Dyson’s Brownian motion models for the standard Gaussian random-matrix ensembles, we report a systematic study of Hermitian matrix-valued processes and their eigenvalue processes associated with the chiral and nonstandard random-matrix ensembles. In addition to the noncolliding Brownian motions, we introduce a one-parameter family of temporally homogeneous noncolliding systems of the Bessel processes and a two-parameter family of temporally inhomogeneous noncolliding systems of Yor’s generalized meanders and show that all of the ten classes of eigenvalue statistics in the Altland–Zirnbauer classification are realized as particle distributions in the special cases of these diffusion particle systems. As a corollary of each equivalence in distribution of a temporally inhomogeneous eigenvalue process and a noncolliding diffusion process, a stochastic-calculus proof of a version of the Harish–Chandra (Itzykson–Zuber) formula of integral over unitary group is established.