LEADER 04344nam 2200685Ia 450 001 9910459302903321 005 20200520144314.0 010 $a1-282-64174-3 010 $a9786612641749 010 $a1-4008-3541-0 024 7 $a10.1515/9781400835416 035 $a(CKB)2670000000031864 035 $a(EBL)557142 035 $a(OCoLC)656260887 035 $a(SSID)ssj0000399557 035 $a(PQKBManifestationID)11257720 035 $a(PQKBTitleCode)TC0000399557 035 $a(PQKBWorkID)10376507 035 $a(PQKB)11093412 035 $a(MiAaPQ)EBC557142 035 $a(DE-B1597)446587 035 $a(OCoLC)979593113 035 $a(DE-B1597)9781400835416 035 $a(Au-PeEL)EBL557142 035 $a(CaPaEBR)ebr10397711 035 $a(CaONFJC)MIL264174 035 $a(EXLCZ)992670000000031864 100 $a20100111d2010 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aLog-gases and random matrices$b[electronic resource] /$fP.J. Forrester 205 $aCourse Book 210 $aPrinceton $cPrinceton University Press$dc2010 215 $a1 online resource (806 p.) 225 1 $aLondon Mathematical Society monographs 300 $aDescription based upon print version of record. 311 $a0-691-12829-4 320 $aIncludes bibliographical references and index. 327 $t Frontmatter -- $tPreface -- $tContents -- $tChapter One. Gaussian Matrix Ensembles -- $tChapter Two. Circular Ensembles -- $tChapter Three. Laguerre And Jacobi Ensembles -- $tChapter Four. The Selberg Integral -- $tChapter Five. Correlation functions at ? = 2 -- $tChapter Six. Correlation Functions At ?= 1 And 4 -- $tChapter Seven. Scaled limits at ? = 1, 2 and 4 -- $tChapter Eight. Eigenvalue probabilities - Painlevé systems approach -- $tChapter Nine. Eigenvalue probabilities- Fredholm determinant approach -- $tChapter Ten. Lattice paths and growth models -- $tChapter Eleven. The Calogero-Sutherland model -- $tChapter Twelve. Jack polynomials -- $tChapter Thirteen. Correlations for general ? -- $tChapter Fourteen. Fluctuation formulas and universal behavior of correlations -- $tChapter Fifteen. The two-dimensional one-component plasma -- $tBibliography -- $tIndex 330 $aRandom matrix theory, both as an application and as a theory, has evolved rapidly over the past fifteen years. Log-Gases and Random Matrices gives a comprehensive account of these developments, emphasizing log-gases as a physical picture and heuristic, as well as covering topics such as beta ensembles and Jack polynomials. Peter Forrester presents an encyclopedic development of log-gases and random matrices viewed as examples of integrable or exactly solvable systems. Forrester develops not only the application and theory of Gaussian and circular ensembles of classical random matrix theory, but also of the Laguerre and Jacobi ensembles, and their beta extensions. Prominence is given to the computation of a multitude of Jacobians; determinantal point processes and orthogonal polynomials of one variable; the Selberg integral, Jack polynomials, and generalized hypergeometric functions; Painlevé transcendents; macroscopic electrostatistics and asymptotic formulas; nonintersecting paths and models in statistical mechanics; and applications of random matrix theory. This is the first textbook development of both nonsymmetric and symmetric Jack polynomial theory, as well as the connection between Selberg integral theory and beta ensembles. The author provides hundreds of guided exercises and linked topics, making Log-Gases and Random Matrices an indispensable reference work, as well as a learning resource for all students and researchers in the field. 410 0$aLondon Mathematical Society monographs. 606 $aRandom matrices 606 $aJacobi polynomials 606 $aIntegral theorems 608 $aElectronic books. 615 0$aRandom matrices. 615 0$aJacobi polynomials. 615 0$aIntegral theorems. 676 $a519.2 700 $aForrester$b Peter$g(Peter John)$0557666 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910459302903321 996 $aLog-gases and random matrices$92476415 997 $aUNINA