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Random Matrices - Madan Lal Mehta

Random Matrices

(Autor)

Buch | Hardcover
688 Seiten
2004 | 3rd edition
Academic Press Inc (Verlag)
978-0-12-088409-4 (ISBN)
CHF 199,95 inkl. MwSt
Gives a description of analytical methods devised to study random matrices. This work reflects the developments in the field. It includes a coverage of skew-orthogonal and bi-orthogonal polynomials and their use in the evaluation of some multiple integrals. It also presents Fredholm determinants and Painleve equations.
Random 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 skew-orthogoanl and bi-orthogonal polynomials, parallel to that of the widely known and used orthogonal polynomials, is explained here for the first time.

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.

Erscheint lt. Verlag 6.10.2004
Reihe/Serie Pure and Applied Mathematics
Verlagsort San Diego
Sprache englisch
Maße 152 x 229 mm
Gewicht 1250 g
Themenwelt Mathematik / Informatik Mathematik Algebra
ISBN-10 0-12-088409-7 / 0120884097
ISBN-13 978-0-12-088409-4 / 9780120884094
Zustand Neuware
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