by Giambattista Giacomin (Université Paris 7 – D Diderot & Laboratoire de Probabilités et Modèles Aléatoires, CNRS — UMR7599, France)

Table of Contents (76k)
Preface (182k)
Chapter 1: Random Polymer Models and their Applications (668k)

This volume introduces readers to the world of disordered systems and to some of the remarkable probabilistic techniques developed in the field. The author explores in depth a class of directed polymer models to which much attention has been devoted in the last 25 years, in particular in the fields of physical and biological sciences. The models treated have been widely used in studying, for example, the phenomena of polymer pinning on a defect line, the behavior of copolymers in proximity to an interface between selective solvents and the DNA denaturation transition. In spite of the apparent heterogeneity of this list, in mathematical terms, a unified vision emerges. One is in fact dealing with the natural statistical mechanics systems built on classical renewal sequences by introducing one-body potentials.

This volume is also a self-contained mathematical account of the state of the art for this class of statistical mechanics models.

• Random Polymer Models and Their Applications
• The Homogeneous Pinning Model
• Weakly Inhomogeneous Models
• The Free Energy of Disordered Polymer Chains
• Disordered Pinning Models: The Phase Diagram
• Disordered Copolymers and Selective Interfaces: The Phase Diagram
• The Localized Phase of Disordered Polymers
• The Delocalized Phase of Disordered Polymers
• Numerical Algorithms and Computations