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  • © 2017

Directed Polymers in Random Environments

École d'Été de Probabilités de Saint-Flour XLVI – 2016

Authors:

  1. Francis Comets

    1. Mathematics, case 7012, Université Paris Diderot - Paris 7, Paris, France

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  • The first book to be devoted to this active field of research in probability and statistical physics

  • Aimed at experienced researchers, but also accessible to masters and Ph.D. students

  • Authored by a leading expert in the subject

  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2175)

Part of the book sub series: École d'Été de Probabilités de Saint-Flour (LNMECOLE)

Sections

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  • ISBN: 978-3-319-50487-2
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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xv
    PDF

  2. Introduction

    • Francis Comets
    Pages 1-12

  3. Thermodynamics and Phase Transition

    • Francis Comets
    Pages 13-29

  4. The Martingale Approach and the L 2 Region

    • Francis Comets
    Pages 31-55

  5. Lattice Versus Tree

    • Francis Comets
    Pages 57-73

  7. The Localized Phase

    • Francis Comets
    Pages 91-106

  8. Log-Gamma Polymer Model

    • Francis Comets
    Pages 107-125

  9. Kardar-Parisi-Zhang Equation and Universality

    • Francis Comets
    Pages 127-146

  10. Variational Formulas

    • Francis Comets
    Pages 147-171

  11. Back Matter

    Pages 173-202
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About this book

Analyzing the phase transition from diffusive to localized behavior in a model of directed polymers in a random environment, this volume places particular emphasis on the localization phenomenon. The main question
is: What does the path of a random walk look like if rewards and penalties are spatially randomly distributed?
This model, which provides a simplified version of stretched elastic chains pinned by random impurities, has attracted much research activity, but it (and its relatives) still holds many secrets, especially in high dimensions. It has non-gaussian scaling limits and it belongs to the so-called KPZ universality class when the space is one-dimensional. Adopting a Gibbsian approach, using general and powerful tools from probability theory, the discrete model is studied in full generality.
 
Presenting the state-of-the art from different perspectives, and written in the form of a first course on the subject, this monograph is aimed at researchers in probability or statistical physics, but is also accessible to masters and Ph.D. students.
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Keywords

  • random polymer models
  • random media
  • localization
  • Kardar-Parisi-Zhang equation
  • pinning transition
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Authors and Affiliations

  • Mathematics, case 7012, Université Paris Diderot - Paris 7, Paris, France

    Francis Comets

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Bibliographic Information

  • Book Title: Directed Polymers in Random Environments

  • Book Subtitle: École d'Été de Probabilités de Saint-Flour XLVI – 2016

  • Authors: Francis Comets

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-50487-2

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing AG 2017

  • Softcover ISBN: 978-3-319-50486-5Published: 01 February 2017

  • eBook ISBN: 978-3-319-50487-2Published: 26 January 2017

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XVI, 199

  • Number of Illustrations: 18 b/w illustrations, 2 illustrations in colour

  • Topics: Probability Theory, Theoretical, Mathematical and Computational Physics

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Access via your institution
eBook USD 39.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-50487-2
  • 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 49.99
Price excludes VAT (USA)
Learn about institutional subscriptions