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Random Matrices

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Title: Random Matrices
Description: 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. - 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 Painlevé 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
Authors: Madan Lal Mehta
Resource Type: eBook.
Subjects: Random matrices
Categories: MATHEMATICS / Algebra / Linear
Database: eBook Collection (EBSCOhost)
FullText Links:
  – Type: ebook-pdf
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  Availability: 0
Header DbId: nlebk
DbLabel: eBook Collection (EBSCOhost)
An: 189456
RelevancyScore: 992
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
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  Data: Random Matrices
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  Data: 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. - 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 Painlevé 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
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RecordInfo BibRecord:
  BibEntity:
    Classifications:
      – Code: 512.55
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Random matrices
        Type: general
    Titles:
      – TitleFull: Random Matrices
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Madan Lal Mehta
      – PersonEntity:
          Name:
            NameFull: Madan Lal Mehta
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      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2004
            – D: 04
              M: 02
              Type: profile
              Y: 2014
          Identifiers:
            – Type: isbn-print
              Value: 9780120884094
            – Type: isbn-electronic
              Value: 9780080474113
          Numbering:
            – Type: volume
              Value: 00142
          Titles:
            – TitleFull: Random Matrices
              Type: main
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