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  • Book
  • © 1993

Products of Random Matrices

in Statistical Physics

Part of the book series: Springer Series in Solid-State Sciences (SSSOL, volume 104)

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  • ISBN: 978-3-642-84942-8
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Table of contents (7 chapters)

  1. Front Matter

    Pages I-XIII
  2. Background

    1. Front Matter

      Pages 1-1
    2. Why Study Random Matrices?

      • Andrea Crisanti, Giovanni Paladin, Angelo Vulpiani
      Pages 3-15
    3. Lyapunov Exponents for PRM

      • Andrea Crisanti, Giovanni Paladin, Angelo Vulpiani
      Pages 17-40
  3. Applications

    1. Front Matter

      Pages 41-41
    2. Chaotic Dynamical Systems

      • Andrea Crisanti, Giovanni Paladin, Angelo Vulpiani
      Pages 43-58
    3. Disordered Systems

      • Andrea Crisanti, Giovanni Paladin, Angelo Vulpiani
      Pages 59-85
    4. Localization

      • Andrea Crisanti, Giovanni Paladin, Angelo Vulpiani
      Pages 87-113
  4. Miscellany

    1. Front Matter

      Pages 115-115
    2. Other Applications

      • Andrea Crisanti, Giovanni Paladin, Angelo Vulpiani
      Pages 117-133
    3. Appendices

      • Andrea Crisanti, Giovanni Paladin, Angelo Vulpiani
      Pages 135-156
  5. Back Matter

    Pages 157-169

About this book

At the present moment, after the success of the renormalization group in providing a conceptual framework for studying second-order phase tran­ sitions, we have a nearly satisfactory understanding of the statistical me­ chanics of classical systems with a non-random Hamiltonian. The situation is completely different if we consider the theory of systems with a random Hamiltonian or of chaotic dynamical systems. The two fields are connected; in fact, in the latter the effects of deterministic chaos can be modelled by an appropriate stochastic process. Although many interesting results have been obtained in recent years and much progress has been made, we still lack a satisfactory understanding of the extremely wide variety of phenomena which are present in these fields. The study of disordered or chaotic systems is the new frontier where new ideas and techniques are being developed. More interesting and deep results are expected to come in future years. The properties of random matrices and their products form a basic tool, whose importance cannot be underestimated. They playa role as important as Fourier transforms for differential equations. This book is extremely interesting as far as it presents a unified approach for the main results which have been obtained in the study of random ma­ trices. It will become a reference book for people working in the subject. The book is written by physicists, uses the language of physics and I am sure that many physicists will read it with great pleasure.

Keywords

  • Lyapunov exponents
  • Products of random matrices
  • chaotic systems
  • deterministic chaos
  • disordered system
  • disordered systems
  • dynamical systems
  • fields
  • mechanics
  • numerical method
  • physics
  • random media
  • statistical mechanics
  • statistical physics
  • wave

Authors and Affiliations

  • Dipartimento di Fisica, Università di Roma, Roma, Italy

    Andrea Crisanti, Angelo Vulpiani

  • Dipartimento di Fisica, Università dell’Aquila, Coppito, L’Aquila, Italy

    Giovanni Paladin

Bibliographic Information

Buying options

eBook USD 109.00
Price excludes VAT (USA)
  • ISBN: 978-3-642-84942-8
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 139.99
Price excludes VAT (USA)