Random Polymers

École d¿Été de Probabilités de Saint-Flour XXXVII ¿ 2007

  • Authors
  • Frank Hollander

Part of the Lecture Notes in Mathematics book series (LNM, volume 1974)

Also part of the Ecole d'Eté Probabilit.Saint-Flour book sub series (LNMECOLE, volume 1974)

Table of contents

  1. Front Matter
    Pages 1-13
  2. Frank den Hollander
    Pages 1-7
  3. Frank den Hollander
    Pages 9-16
  4. Polymers with Self-Interaction

    1. Front Matter
      Pages 17-18
    2. Frank den Hollander
      Pages 19-39
    3. Frank den Hollander
      Pages 41-58
    4. Frank den Hollander
      Pages 59-65
    5. Frank den Hollander
      Pages 67-84
    6. Frank den Hollander
      Pages 85-112
  5. Polymers in Random Environment

    1. Front Matter
      Pages 113-114
    2. Frank den Hollander
      Pages 115-127
    3. Frank den Hollander
      Pages 129-154
    4. Frank den Hollander
      Pages 155-179
    5. Frank den Hollander
      Pages 181-204
    6. Frank den Hollander
      Pages 205-231
  6. Back Matter
    Pages 1-31

About this book

Introduction

Polymer chains that interact with themselves and/or with their environment are fascinating objects, displaying a range of interesting physical and chemical phenomena. The focus in this monograph is on the mathematical description of some of these phenomena, with particular emphasis on phase transitions as a function of interaction parameters, associated critical behavior and space-time scaling. Topics include: self-repellent polymers, self-attracting polymers, polymers interacting with interfaces, charged polymers, copolymers near linear or random selective interfaces, polymers interacting with random substrate and directed polymers in random environment. Different techniques are exposed, including the method of local times, large deviations, the lace expansion, generating functions, the method of excursions, ergodic theory, partial annealing estimates, coarse-graining techniques and martingales. Thus, this monograph offers a mathematical panorama of polymer chains, which even today holds plenty of challenges.

Keywords

Ergodic theory Martingale large deviations local time phase transition phase transitions polymers random environment scaling

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-00333-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2009
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-00332-5
  • Online ISBN 978-3-642-00333-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book
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