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Random matrices

Mehta, M. L.

Random matrices

Record Type:	Electronic resources : Monograph/item
Title/Author:	Random matricesMadan Lal Mehta.
Author:	Mehta, M. L.
Published:	Amsterdam ;Elsevier/Academic Press,2004.
Description:	xviii, 688 p. :ill. ;24 cm.
Subject:	Random matrices.
Online resource:	An electronic book accessible through the World Wide Web; click for information
Online resource:	http://www.engineeringvillage.com/controller/servlet/OpenURL?genre=book&isbn=9780120884094
ISBN:	9780120884094

Random matrices
Mehta, M. L.

Random matrices[electronic resource] /Madan Lal Mehta. - 3rd ed. - Amsterdam ;Elsevier/Academic Press,2004. - xviii, 688 p. :ill. ;24 cm. - Pure and applied mathematics ;v. 142. - Pure and applied mathematics (Academic Press) ;140..

Includes bibliographical references (p. 655-679) and indexes.

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.

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. Presentation of many new results in one place for the first time. First time coverage of skew-orthogonal and bi-orthogonal polynomials and their use in the evaluation of some multiple integrals. Fredholm determinants and Painle�v equations. The three Gaussian ensembles (unitary, orthogonal, and symplectic); their n-point correlations, spacing probabilities. Fredholm determinants and inverse scattering theory. Probability densities of random determinants.

Electronic reproduction.
Amsterdam :
Elsevier Science & Technology,
2007.

Mode of access: World Wide Web.

ISBN: 9780120884094

Source: 106526:106558Elsevier Science & Technologyhttp://www.sciencedirect.comSubjects--Topical Terms:

240098
Random matrices.
Index Terms--Genre/Form:

214472
Electronic books.

LC Class. No.: QA188 / .M445 2004eb

Dewey Class. No.: 512.9

Random matrices
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020 $a 9780120884094
020 $a 0120884097
029 1 $a NZ1 $b 12434397
035 $a (OCoLC)162130088
035 $a ocn162130088
037 $a 106526:106558 $b Elsevier Science & Technology $n http://www.sciencedirect.com
040 $a OPELS $c OPELS $d OPELS
049 $a TEFA
050 1 4 $a QA188 $b .M445 2004eb
082 0 4 $a 512.9 $2 22
100 1 $a Mehta, M. L. $3 455066
245 1 0 $a Random matrices $h [electronic resource] / $c Madan Lal Mehta.
250 $a 3rd ed.
260 $a Amsterdam ; $a San Diego, CA : $b Elsevier/Academic Press, $c 2004.
300 $a xviii, 688 p. : $b ill. ; $c 24 cm.
490 1 $a Pure and applied mathematics ; $v v. 142
504 $a Includes bibliographical references (p. 655-679) and indexes.
505 0 $a 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.
520 $a 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. Presentation of many new results in one place for the first time. First time coverage of skew-orthogonal and bi-orthogonal polynomials and their use in the evaluation of some multiple integrals. Fredholm determinants and Painle�v equations. The three Gaussian ensembles (unitary, orthogonal, and symplectic); their n-point correlations, spacing probabilities. Fredholm determinants and inverse scattering theory. Probability densities of random determinants.
533 $a Electronic reproduction. $b Amsterdam : $c Elsevier Science & Technology, $d 2007. $n Mode of access: World Wide Web. $n System requirements: Web browser. $n Title from title screen (viewed on July 25, 2007). $n Access may be restricted to users at subscribing institutions.
650 0 $a Random matrices. $3 240098
650 6 $a Matrices al�eatoires. $3 455067
650 7 $a Mec�anica estat�istica. $2 larpcal $3 455068
655 7 $a Electronic books. $2 local. $3 214472
710 2 $a ScienceDirect (Online service) $3 307425
776 1 $c Original $z 0120884097 $z 9780120884094 $w (OCoLC)56987512
830 0 $a Pure and applied mathematics (Academic Press) ; $v 140. $3 441190
856 4 0 $3 ScienceDirect $u http://www.sciencedirect.com/science/publication?issn=00798169&volume=142 $z An electronic book accessible through the World Wide Web; click for information
856 4 0 $3 Referex $u http://www.engineeringvillage.com/controller/servlet/OpenURL?genre=book&isbn=9780120884094 $z An electronic book accessible through the World Wide Web; click for information
994 $a C0 $b TEF

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