04344nam 2200685Ia 450 991045930290332120200520144314.01-282-64174-397866126417491-4008-3541-010.1515/9781400835416(CKB)2670000000031864(EBL)557142(OCoLC)656260887(SSID)ssj0000399557(PQKBManifestationID)11257720(PQKBTitleCode)TC0000399557(PQKBWorkID)10376507(PQKB)11093412(MiAaPQ)EBC557142(DE-B1597)446587(OCoLC)979593113(DE-B1597)9781400835416(Au-PeEL)EBL557142(CaPaEBR)ebr10397711(CaONFJC)MIL264174(EXLCZ)99267000000003186420100111d2010 uy 0engur|n|---|||||txtccrLog-gases and random matrices[electronic resource] /P.J. ForresterCourse BookPrinceton Princeton University Pressc20101 online resource (806 p.)London Mathematical Society monographsDescription based upon print version of record.0-691-12829-4 Includes bibliographical references and index. Frontmatter -- Preface -- Contents -- Chapter One. Gaussian Matrix Ensembles -- Chapter Two. Circular Ensembles -- Chapter Three. Laguerre And Jacobi Ensembles -- Chapter Four. The Selberg Integral -- Chapter Five. Correlation functions at β = 2 -- Chapter Six. Correlation Functions At β= 1 And 4 -- Chapter Seven. Scaled limits at β = 1, 2 and 4 -- Chapter Eight. Eigenvalue probabilities - Painlevé systems approach -- Chapter Nine. Eigenvalue probabilities- Fredholm determinant approach -- Chapter Ten. Lattice paths and growth models -- Chapter Eleven. The Calogero-Sutherland model -- Chapter Twelve. Jack polynomials -- Chapter Thirteen. Correlations for general β -- Chapter Fourteen. Fluctuation formulas and universal behavior of correlations -- Chapter Fifteen. The two-dimensional one-component plasma -- Bibliography -- IndexRandom matrix theory, both as an application and as a theory, has evolved rapidly over the past fifteen years. Log-Gases and Random Matrices gives a comprehensive account of these developments, emphasizing log-gases as a physical picture and heuristic, as well as covering topics such as beta ensembles and Jack polynomials. Peter Forrester presents an encyclopedic development of log-gases and random matrices viewed as examples of integrable or exactly solvable systems. Forrester develops not only the application and theory of Gaussian and circular ensembles of classical random matrix theory, but also of the Laguerre and Jacobi ensembles, and their beta extensions. Prominence is given to the computation of a multitude of Jacobians; determinantal point processes and orthogonal polynomials of one variable; the Selberg integral, Jack polynomials, and generalized hypergeometric functions; Painlevé transcendents; macroscopic electrostatistics and asymptotic formulas; nonintersecting paths and models in statistical mechanics; and applications of random matrix theory. This is the first textbook development of both nonsymmetric and symmetric Jack polynomial theory, as well as the connection between Selberg integral theory and beta ensembles. The author provides hundreds of guided exercises and linked topics, making Log-Gases and Random Matrices an indispensable reference work, as well as a learning resource for all students and researchers in the field.London Mathematical Society monographs.Random matricesJacobi polynomialsIntegral theoremsElectronic books.Random matrices.Jacobi polynomials.Integral theorems.519.2Forrester Peter(Peter John)557666MiAaPQMiAaPQMiAaPQBOOK9910459302903321Log-gases and random matrices2476415UNINA01036nam0 22002651i 450 VAN004830120060721120000.020060721d1966 |0itac50 baitaIT|||| |||||Antonio Rizzo[a cura di Giovanni Mariacher]MilanoFabbric1966[4] c., XVI p. di tav.in gran parte ill.36 cm.001VAN00481182001 ˆI ‰maestri della scultura210 MilanoFabbri.35MilanoVANL000284RizzoAntonioVANV03835181731MariacherGiovanniVANV031760Fabbri, FabrizioVANV108057650ITSOL20230616RICABIBLIOTECA DEL DIPARTIMENTO DI LETTERE E BENI CULTURALIIT-CE0103VAN07VAN0048301BIBLIOTECA DEL DIPARTIMENTO DI LETTERE E BENI CULTURALI07CONS Pc 2 35 07 53752 20060721 Antonio Rizzo1016272UNICAMPANIA