Directed Polymers in Random Environments

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

  • Francis Comets

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

Also part of the École d'Été de Probabilités de Saint-Flour book sub series (LNMECOLE, volume 2175)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Francis Comets
    Pages 1-12
  3. Francis Comets
    Pages 13-29
  4. Francis Comets
    Pages 31-55
  5. Francis Comets
    Pages 57-73
  6. Francis Comets
    Pages 91-106
  7. Francis Comets
    Pages 107-125
  8. Francis Comets
    Pages 127-146
  9. Francis Comets
    Pages 147-171
  10. Back Matter
    Pages 173-202

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.


random polymer models random media localization Kardar-Parisi-Zhang equation pinning transition

Authors and affiliations

  • Francis Comets
    • 1
  1. 1.Mathematics, case 7012Université Paris Diderot - Paris 7ParisFrance

Bibliographic information