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010   $a981-10-3316-1
024 7 $a10.1007/978-981-10-3316-2
035   $a(CKB)3710000001022115
035   $a(MiAaPQ)EBC4787321
035   $a(DE-He213)978-981-10-3316-2
035   $a(PPN)198338899
035   $a(EXLCZ)993710000001022115
100   $a20170113d2016      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $2rdacontent
182   $2rdamedia
183   $2rdacarrier
200 10$aRandom matrix theory with an external source /$fby Edouard Brézin, Shinobu Hikami
205   $a1st ed. 2016.
210  1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2016.
215   $a1 online resource (143 pages)
225 1 $aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v19
311 08$a981-10-3315-3 
320   $aIncludes bibliographical references and index.
330   $aThis is a first book to show that the theory of the Gaussian random matrix is essential to understand the universal correlations with random fluctuations and to demonstrate that it is useful to evaluate topological universal quantities. We consider Gaussian random matrix models in the presence of a deterministic matrix source. In such models the correlation functions are known exactly for an arbitrary source and for any size of the matrices. The freedom given by the external source allows for various tunings to different classes of universality. The main interest is to use this freedom to compute various topological invariants for surfaces such as the intersection numbers for curves drawn on a surface of given genus with marked points, Euler characteristics, and the Gromov?Witten invariants. A remarkable duality for the average of characteristic polynomials is essential for obtaining such topological invariants. The analysis is extended to nonorientable surfaces and to surfaces with boundaries.
410  0$aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v19
606   $aMathematical physics
606   $aStatistical physics
606   $aTopological groups
606   $aLie groups
606   $aNuclear physics
606   $aDynamics
606   $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000
606   $aStatistical Physics and Dynamical Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P19090
606   $aTopological Groups, Lie Groups$3https://scigraph.springernature.com/ontologies/product-market-codes/M11132
606   $aParticle and Nuclear Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P23002
606   $aComplex Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P33000
615  0$aMathematical physics.
615  0$aStatistical physics.
615  0$aTopological groups.
615  0$aLie groups.
615  0$aNuclear physics.
615  0$aDynamics.
615 14$aMathematical Physics.
615 24$aStatistical Physics and Dynamical Systems.
615 24$aTopological Groups, Lie Groups.
615 24$aParticle and Nuclear Physics.
615 24$aComplex Systems.
676   $a512.9434
700   $aBre?zin$b E.$4aut$4http://id.loc.gov/vocabulary/relators/aut$053516
702   $aHikami$b Shinobu$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a9910163096303321
996   $aRandom Matrix Theory with an External Source$92070238
997   $aUNINA