Macedo-Junior, A. F.; Macêdo, A. M. S. Brownian-motion ensembles of random matrix theory: a classification scheme and an integral transform method. (English) Zbl 1215.82039 Nucl. Phys., B 752, No. 3, 439-475 (2006). Summary: We study a class of Brownian-motion ensembles obtained from the general theory of Markovian stochastic processes in random-matrix theory. The ensembles admit a complete classification scheme based on a recent multivariable generalization of classical orthogonal polynomials and are closely related to Hamiltonians of Calogero-Sutherland-type quantum systems. An integral transform is proposed to evaluate the \(n\)-point correlation function for a large class of initial distribution functions. Applications of the classification scheme and of the integral transform to concrete physical systems are presented in detail. Cited in 3 Documents MSC: 82C41 Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics 33C90 Applications of hypergeometric functions 81R12 Groups and algebras in quantum theory and relations with integrable systems 82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics Keywords:random-matrix; Fokker-Planck equation; Calogero; Sutherland model; multivariate orthogonal polynomials; quantum chaos; mesoscopic physics PDF BibTeX XML Cite \textit{A. F. Macedo-Junior} and \textit{A. M. S. Macêdo}, Nucl. Phys., B 752, No. 3, 439--475 (2006; Zbl 1215.82039) Full Text: DOI References: [1] Okolowicz, J.; Ploszajczak, M.; Rotter, I., Phys. rep., 374, 271, (2003) [2] Ferry, D.K.; Goodnick, S.M., Transport in nanostructures, (1997), Cambridge Univ. Press Cambridge [3] Stöckmann, H.-J., Quantum chaos: an introduction, (2000), Cambridge Univ. 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