Random MatricesRandom Matrices gives a coherent and detailed description of analytical methods devised to study random matrices. These methods are critical to the understanding of various fields in in mathematics and mathematical physics, such as nuclear excitations, ultrasonic resonances of structural materials, chaotic systems, the zeros of the Riemann and other zeta functions. More generally they apply to the characteristic energies of any sufficiently complicated system and which have found, since the publication of the second edition, many new applications in active research areas such as quantum gravity, traffic and communications networks or stock movement in the financial markets. This revised and enlarged third edition reflects the latest developements in the field and convey a greater experience with results previously formulated. For example, the theory of skeworthogoanl and biorthogonal polynomials, parallel to that of the widely known and used orthogonal polynomials, is explained here for the first time.

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Contents
1  
33  
50  
63  
71  
Chapter 6 Gaussian Unitary Ensemble  110 
Chapter 7 Gaussian Orthogonal Ensemble  146 
Chapter 8 Gaussian Symplectic Ensemble  175 
Chapter 18 Asymptotic Behaviour of Eβ 0 s by Inverse Scattering  335 
Chapter 19 Matrix Ensembles and Classical Orthogonal Polynomials  354 
Chapter 20 Level Spacing Functions Eβr s Interrelations and Power Series Expansions  365 
Chapter 21 Fredholm Determinants and Painlev Equations  382 
Chapter 22 Moments of the Characteristic Polynomial in the Three Ensembles of Random Matrices  409 
Chapter 23 Hermitian Matrices Coupled in a Chain  426 
Chapter 24 Gaussian Ensembles Edge of the Spectrum  449 
Chapter 25 Random Permutations Circular Unitary Ensemble CUE and Gaussian Unitary Ensemble GUE  460 
Brownian Motion Model  182 
Chapter 10 Circular Ensembles  191 
Chapter 11 Circular Ensembles Continued  203 
Chapter 12 Circular Ensembles Thermodynamics  224 
Chapter 13 Gaussian Ensemble of AntiSymmetric Hermitian Matrices  237 
Chapter 14 A Gaussian Ensemble of Hermitian Matrices With Unequal Real and Imaginary Parts  244 
Chapter 15 Matrices With Gaussian Element Densities But With No Unitary or Hermitian Conditions Imposed  266 
Chapter 16 Statistical Analysis of a LevelSequence  287 
Chapter 17 Selbergs Integral and Its Consequences  309 
Chapter 26 Probability Densities of the Determinants Gaussian Ensembles  469 
Chapter 27 Restricted Trace Ensembles  487 
Appendices  494 
Notes  645 
655  
680  
684  
Other editions  View all
Pure and Applied Mathematics: A Series of Monographs and Textbooks M. L. Mehta No preview available  2004 