%0 Journal Article %1 borodin06 %A Borodin, A. %A Strahov, E. %D 2006 %I Wiley Subscription Services, Inc., A Wiley Company %J Communications on Pure and Applied Mathematics %K rando_matrix %N 2 %P 161--253 %R 10.1002/cpa.20092 %T Averages of Characteristic Polynomials in Random Matrix Theory %V 59 %X 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.

@article{borodin06, abstract = {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.}, added-at = {2014-03-28T17:32:38.000+0100}, author = {Borodin, A. and Strahov, E.}, biburl = {https://www.bibsonomy.org/bibtex/2fdb966862e1824de19af5ca55da644c2/ytyoun}, doi = {10.1002/cpa.20092}, interhash = {0230d45132f1cae04f2dd532a7922586}, intrahash = {fdb966862e1824de19af5ca55da644c2}, issn = {1097-0312}, journal = {Communications on Pure and Applied Mathematics}, keywords = {rando_matrix}, number = 2, pages = {161--253}, publisher = {Wiley Subscription Services, Inc., A Wiley Company}, timestamp = {2014-03-28T17:32:38.000+0100}, title = {Averages of Characteristic Polynomials in Random Matrix Theory}, volume = 59, year = 2006 }