Random matrices

Random matrices

by Mehta, M. L.

Type Book
Rate 0.0 /5

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 publicati…

Read More ↓
Details
Files
Reviews
Download

Title Statements

  • Full title :Random matrices / Madan Lal Mehta.

Summary

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 Painlev̌ 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.

Read More ↓

Edition Statements

  • Publication Date:2004.
  • Edition:3rd ed

Publication Statements

  • Publisher(s):Academic Press
  • Place of Publication:Amsterdam
  • Language:eng
  • Publication Date:2004.

Notes

Title from e-book title screen (viewed November 15, 2007).

The Physical Object

  • Description:1 online resource (xviii, 688 pages : : illustrations

Edition Identifiers

  • ISBN:008047411X, 9780080474113, 9780120884094, 0120884097, 9780125660501, 0125660502
  • oclc:ocn317384419
  • LC Classification:QA188
  • Dewey Decimal:512.9434

Table of Contents

Cover -- Contents -- Preface to the Third Edition -- Preface to the Second Edition -- Preface to the First Edition -- Introduction -- Random Matrices in Nuclear Physics -- Random Matrices in Other Branches of Knowledge -- A Summary of Statistical Facts about Nuclear Energy Levels -- Level Density -- Distribution of Neutron Widths -- Radiation and Fission Widths -- Level Spacings -- Definition of a Suitable Function for the Study of Level Correlations -- Wigner Surmise -- Electromagnetic Properties of Small Metallic Particles -- Analysis of Experimental Nuclear Levels -- The Zeros of The Riemann Zeta Function -- Things Worth Consideration, But Not Treated in This Book -- Gaussian Ensembles. The Joint Probability Density Function for the Matrix Elements -- Preliminaries -- Time-Reversal Invariance -- Gaussian Orthogonal Ensemble -- Gaussian Symplectic Ensemble -- Gaussian Unitary Ensemble -- Joint Probability Density Function for the Matrix Elements -- Gaussian Ensemble of Hermitian Matrices With Unequal Real and Imaginary Parts -- Anti-Symmetric Hermitian Matrices -- Summary of Chapter 2 -- Gaussian Ensembles. The Joint Probability Density Function for the Eigenvalues -- Orthogonal…

Read More ↓

Subjects

MATHEMATICS -- Matrices Matrices aléatoires Mecanica estatistica Random matrices

Writers

Mehta, M. L.

More from this Series

  • Introduction to Lie groups and Lie algebras

    1973.
    more →
    Introduction to Lie groups and Lie algebras

  • Introduction to Lie groups and Lie algebras

    c1973.
    more →

  • Introduction to Lie groups and Lie algebras

    1973.
    more →
    Introduction to Lie groups and Lie algebras

  • Introduction to lie groups and lie algebras

    1973.
    more →
    Introduction to lie groups and lie algebras

  • Introduction to Lie groups and Lie algebras

    1973.
    more →
    Introduction to Lie groups and Lie algebras

Rate & Review

0.0/5
(0 people Voted)

No reviews yet. Be the first to rate this work.

Files & Downloads

  • Random matrices -- (.djvu)

    DJVU · 5.0 MB · updated
    Login →

  • Quantum mechanics in Hilbert space -- (.djvu)

    DJVU · 4.5 MB · updated
    Login →

  • Random matrices -- (.djvu)

    DJVU · 10.7 MB · updated
    Login →

  • Quantum mechanics in Hilbert space -- (.pdf)

    PDF · 43.4 MB · updated
    Login →

  • Random Matrices -- (.pdf)

    PDF · 6.7 MB · updated
    Login →

  • Random Matrices -- (.pdf)

    PDF · 2.9 MB · updated
    Login →

  • Random matrices -- (.djvu)

    DJVU · 12.2 MB · updated
    Login →