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Random Matrix Theory (random + matrix_theory)
Selected AbstractsIntegrable operators and canonical differential systemsMATHEMATISCHE NACHRICHTEN, Issue 1-2 2007Lev Sakhnovich Abstract In this article we consider a class of integrable operators and investigate its connections with the following theories: the spectral theory of the non-self-adjoint operators, the Riemann-Hilbert problem, the canonical differential systems, the random matrices theory and the limit values of the multiplicative integral. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Generalized probabilistic approach of uncertainties in computational dynamics using random matrices and polynomial chaos decompositionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2010Christian Soize Abstract A new generalized probabilistic approach of uncertainties is proposed for computational model in structural linear dynamics and can be extended without difficulty to computational linear vibroacoustics and to computational non-linear structural dynamics. This method allows the prior probability model of each type of uncertainties (model-parameter uncertainties and modeling errors) to be separately constructed and identified. The modeling errors are not taken into account with the usual output-prediction-error method, but with the nonparametric probabilistic approach of modeling errors recently introduced and based on the use of the random matrix theory. The theory, an identification procedure and a numerical validation are presented. Then a chaos decomposition with random coefficients is proposed to represent the prior probabilistic model of random responses. The random germ is related to the prior probability model of model-parameter uncertainties. The random coefficients are related to the prior probability model of modeling errors and then depends on the random matrices introduced by the nonparametric probabilistic approach of modeling errors. A validation is presented. Finally, a future perspective is introduced when experimental data are available. The prior probability model of the random coefficients can be improved in constructing a posterior probability model using the Bayesian approach. Copyright © 2009 John Wiley & Sons, Ltd. [source] Transition between Airy1 and Airy2 processes and TASEP fluctuationsCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 11 2008Alexei Borodin We consider the totally asymmetric simple exclusion process, a model in the KPZ universality class. We focus on the fluctuations of particle positions, starting with certain deterministic initial conditions. For large time t, one has regions with constant and linearly decreasing density. The fluctuations on these two regions are given by the Airy1 and Airy2 processes, whose one-point distributions are the GOE and GUE Tracy-Widom distributions of random matrix theory. In this paper we analyze the transition region between these two regimes and obtain the transition process. Its one-point distribution is a new interpolation between GOE and GUE edge distributions. © 2007 Wiley Periodicals, Inc. [source] Averages of characteristic polynomials in random matrix theoryCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 2 2006A. Borodin We compute averages of products and ratios of characteristic polynomials associated with orthogonal, unitary, and symplectic ensembles of random matrix theory. The Pfaffian/determinantal formulae for these averages are obtained, and the bulk scaling asymptotic limits are found for ensembles with Gaussian weights. Classical results for the correlation functions of the random matrix ensembles and their bulk scaling limits are deduced from these formulae by a simple computation. We employ a discrete approximation method: the problem is solved for discrete analogues of random matrix ensembles originating from representation theory, and then a limit transition is performed. Exact Pfaffian/determinantal formulae for the discrete averages are proven using standard tools of linear algebra; no application of orthogonal or skew-orthogonal polynomials is needed. © 2005 Wiley Periodicals, Inc. [source] | ||||||||||