Preface |
Random Polymer Models and their Applications / 1: |
Random Polymers and (De)Localization Phenomena / 1.1: |
A First Model: Pinning on a Defect Line / 1.2: |
Pinning a walk on a defect line / 1.2.1: |
Pinning more general processes on a defect line / 1.2.2: |
Entropic Repulsion and Wetting Phenomena / 1.3: |
Walls versus penetrable substrates / 1.3.1: |
The Denaturation Transition: Poland-Scheraga Models / 1.4: |
Force Induced Unzipping / 1.5: |
Inhomogeneous Charge Distributions: Copolymers and Pinning / 1.6: |
Periodic pinning models / 1.6.1: |
Copolymers, periodic copolymers and selective interfaces / 1.6.2: |
Copolymers with adsorption / 1.6.3: |
Fully Inhomogeneous Charge Distributions and Disordered Polymer Models / 1.7: |
Annealed models / 1.7.1: |
On the Return Time Viewpoint / 1.8: |
On Related Classes of Models / 1.9: |
More general return times / 1.9.1: |
Rewards and penalties on general structures / 1.9.2: |
Bibliographic Complements / 1.10: |
The Homogeneous Pinning Model / 2: |
The Free Energy / 2.1: |
Renewal Theory and Sharp Estimates / 2.2: |
Path Properties: The Infinite Volume Limit / 2.3: |
Path Properties: The Scaling Limit / 2.4: |
Weakly Inhomogeneous Models / 2.5: |
A Formula for the Free Energy: Reduction to a Finite Dimension Problem / 3.1: |
Sharp Estimates on the Partition Function / 3.2: |
The Limit Path Trajectories / 3.3: |
The infinite volume limit / 3.3.1: |
The scaling limit / 3.3.2: |
First Order Transitions, Non-Uniqueness and Phase Diagrams / 3.4: |
The Free Energy of Disordered Polymer Chains / 3.5: |
Preliminary Observations / 4.1: |
Existence of the Free Energy and Self-Averaging / 4.2: |
Periodic versus Disordered Charge Sequences / 4.3: |
Alternative Approaches to the Existence of the Free Energy / 4.4: |
Concentration inequalities and self-averaging / 4.4.1: |
The Super-Additive Ergodic Theorem approach / 4.4.2: |
Disordered Pinning Models: The Phase Diagram / 4.5: |
Preliminary Observations on the Free Energy / 5.1: |
An Improved Lower Bound on the Free Energy / 5.2: |
On the Upper Bound: Annealing and Constrained Annealing / 5.3: |
The Effect of the Disorder on the Order of the Transition: A Smoothing Inequality / 5.4: |
What is One Expecting: The Renormalization Group Viewpoint and the Harris Criterion / 5.5: |
A Fully Inhomogeneous Non-Disordered Model / 5.6: |
Disordered Copolymers and Selective Interfaces: The Phase Diagram / 5.7: |
Copolymers and Homogeneous Localization / 6.1: |
Rare Stretch Strategy for Localization Estimates / 6.2: |
The Weak Coupling Limit: Brownian Motion Model and Universality / 6.3: |
On more general copolymer models and the Brownian scaling / 6.3.1: |
The Localized Phase of Disordered Polymers / 6.3.2: |
A First Tightness Estimate / 7.1: |
Quenched versus Quenched Averaged Estimates / 7.2: |
Quenched Averaged Estimates and the Infinite Volume Polymer Measure / 7.3: |
The Delocalized Phase of Disordered Polymers / 7.4: |
Large Deviations and Delocalization / 8.1: |
Beyond Large Deviations: O(log N) Results / 8.2: |
The Strongly Delocalized Regime / 8.3: |
Numerical Algorithms and Computations / 8.4: |
Computing the Partition Function / 9.1: |
Random walk models / 9.1.1: |
General renewal models / 9.1.2: |
The Fixman-Freire Algorithm / 9.1.3: |
A Statistical Test for Localization / 9.2: |
Applications: A Few Examples / 9.3: |
Mathematical Tools / 9.4: |
Limit Theorems in Probability / A.1: |
Some remarks on convexity / A.1.1: |
Entropy / A.2: |
Concentration Properties / A.3: |
Slow Variation and Laplace Transforms / A.4: |
Renewal Theory for N Valued Random Variables / A.5: |
The renewal theorem / A.5.1: |
The renewal mass function: Transient case / A.5.2: |
The renewal mass function: Null recurrent case / A.5.3: |
Scaling limits of renewal processes / A.5.4: |
Random Walks / A.6: |
The Super-Additive Ergodic Theorem / A.7: |
Perron-Frobenius Theory / A.8: |
Some Technical Estimates / Appendix B: |
Homogeneous Localization Strategy: The Entropy Density / B.1: |
The Weak Localization Limit / B.2: |
Localization and Loss of Memory / B.3: |
Effective Interface Models / Appendix C: |
Ising Model, Effective Interface Models and Random Walks / C.1: |
Bibliography |
Index |
Preface |
Random Polymer Models and their Applications / 1: |
Random Polymers and (De)Localization Phenomena / 1.1: |
A First Model: Pinning on a Defect Line / 1.2: |
Pinning a walk on a defect line / 1.2.1: |
Pinning more general processes on a defect line / 1.2.2: |