This book 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 skew-orthogoanl and bi-orthogonal polynomials, parallel to that of the widely known and used orthogonal polynomials, is explained here for the first time.
ˇ Presentation of many new results in one place for the first time.
ˇ First time coverage of skew-orthogonal and bi-orthogonal polynomials and their use in the evaluation of some multiple integrals.
ˇ Fredholm determinants and Painlevé equations.
ˇ The three Gaussian ensembles (unitary, orthogonal, and symplectic); their n-point correlations, spacing probabilities.
ˇ Fredholm determinants and inverse scattering theory.
ˇ Probability densities of random determinants.
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下载地址： http://uploadphiles.com/index.php?page=main&id=9e77a839&name=Random_Matrices__2Ed____AC__1991__293_d__.zip http://lib.org.by/info/M_Mathematics/MC_Calculus/MCat_Advanced%20calculus/Mehta%20M.L.%20Random%20matrices%20(3ed.,%20Elsevier,%202004)(ISBN%200120884097)(KA)(600dpi)(T)(704s)_MCat_.djvu
Chapter 6 Gaussian Unitary Ensemble
Chapter 7 Gaussian Orthogonal Ensemble
Chapter 8 Gaussian Symplectic Ensemble
Chapter 18 Asymptotic Behaviour of Eβ 0 s by Inverse Scattering
Chapter 19 Matrix Ensembles and Classical Orthogonal Polynomials
Chapter 20 Level Spacing Functions Eβr s Interrelations and Power Series Expansions
Chapter 21 Fredholm Determinants and Painlev Equations
Chapter 22 Moments of the Characteristic Polynomial in the Three Ensembles of Random Matrices
Chapter 23 Hermitian Matrices Coupled in a Chain
Chapter 24 Gaussian Ensembles Edge of the Spectrum
Chapter 25 Random Permutations Circular Unitary Ensemble CUE and Gaussian Unitary Ensemble GUE
Brownian Motion Model
Chapter 10 Circular Ensembles
Chapter 11 Circular Ensembles Continued
Chapter 12 Circular Ensembles Thermodynamics
Chapter 13 Gaussian Ensemble of AntiSymmetric Hermitian Matrices
Chapter 14 A Gaussian Ensemble of Hermitian Matrices With Unequal Real and Imaginary Parts
Chapter 15 Matrices With Gaussian Element Densities But With No Unitary or Hermitian Conditions Imposed
Chapter 16 Statistical Analysis of a LevelSequence
Chapter 17 Selbergs Integral and Its Consequences