Random Matrices

Gives a description of analytical methods devised to study random matrices. This book presents methods, which help in the understanding of various fields in mathematical physics, such as nuclear excitations, ultrasonic resonances of structural materials, and more. It also explains the theory of skew-orthogonal and bi-orthogonal polynomials.

Inhalt
Gaussian Ensembles. The Joint Probability Density Function of the Matrix Elements. Gaussian Ensembles. The Joint Probability Density Function of the Eigenvalues. Gaussian Ensembles. Level Density. Gaussian Unitary Ensemble. Gaussian Orthogonal Ensemble. Gaussian Symplectic Ensemble. Brownian Motion Model. Circular Ensembles. Circular Ensembles (Continued). Circular Ensembles. Thermodynamics. Asymptotic Behaviour of B(O,s) for Large S. Gaussian Ensemble of Anti-Symmetric Hermitian Matrices. Another Gaussian Ensemble of Hermitian Matrices. Matrices with Gaussian Element Densities but with No Unitary or Hermitian Condition Imposed. Statistical Analysis of a Level Sequence. Selberg's Integral and Its Consequences. Gaussian Ensembles. Level Density in the Tail of the Semi-Circle. Restricted Trace Ensembles. Bordered Matrices. Invariance Hypothesis and Matrix Element Correlations. Index.

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