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Products of Random Matrices

in Statistical Physics

  • Andrea Crisanti
  • Giovanni Paladin
  • Angelo Vulpiani

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

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Background

    1. Front Matter
      Pages 1-1
    2. Andrea Crisanti, Giovanni Paladin, Angelo Vulpiani
      Pages 3-15
    3. Andrea Crisanti, Giovanni Paladin, Angelo Vulpiani
      Pages 17-40
  3. Applications

    1. Front Matter
      Pages 41-41
    2. Andrea Crisanti, Giovanni Paladin, Angelo Vulpiani
      Pages 43-58
    3. Andrea Crisanti, Giovanni Paladin, Angelo Vulpiani
      Pages 59-85
    4. Andrea Crisanti, Giovanni Paladin, Angelo Vulpiani
      Pages 87-113
  4. Miscellany

    1. Front Matter
      Pages 115-115
    2. Andrea Crisanti, Giovanni Paladin, Angelo Vulpiani
      Pages 117-133
    3. Andrea Crisanti, Giovanni Paladin, Angelo Vulpiani
      Pages 135-156
  5. Back Matter
    Pages 157-169

About this book

Introduction

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

  • Andrea Crisanti
    • 1
  • Giovanni Paladin
    • 2
  • Angelo Vulpiani
    • 1
  1. 1.Dipartimento di FisicaUniversità di RomaRomaItaly
  2. 2.Dipartimento di FisicaUniversità dell’AquilaCoppito, L’AquilaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-84942-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-84944-2
  • Online ISBN 978-3-642-84942-8
  • Series Print ISSN 0171-1873
  • Buy this book on publisher's site