Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems

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dc.creatorKatori, Makoto
dc.creatorTanemura, Hideki
dc.date2004-02-23
dc.date2004-06-15
dc.date.accessioned2026-07-25T22:26:58Z
dc.descriptionAs 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.
dc.descriptionLaTeX, 27 pages, 4 figures, v3: Minor corrections made for publication in J. Math. Phys
dc.identifierhttps://arxiv.org/abs/math-ph/0402061
dc.identifierhttp://arxiv.org/abs/math-ph/0402061
dc.identifierJ. Math. Phys. 45 (2004) 3058-3085
dc.identifierdoi:10.1063/1.1765215
dc.identifier.urihttps://dspace.dare.co.zw/handle/123456789/89164
dc.subjectMathematical Physics
dc.subjectStatistical Mechanics
dc.subjectProbability
dc.titleSymmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems
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