Random Polymers: École d’Été de Probabilités de Saint-Flour XXXVII – 2007 (Lecture Notes in Mathematics Book 1974)

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. Front Matter....Pages 1-13 Introduction....Pages 1-7 Two Basic Models....Pages 9-16 Front Matter....Pages 17-18 Soft Polymers in Low Dimension....Pages 19-39 Soft Polymers in High Dimension....Pages 41-58 Elastic Polymers....Pages 59-65 Polymer Collapse....Pages 67-84 Polymer Adsorption....Pages 85-112 Front Matter....Pages 113-114 Charged Polymers....Pages 115-127 Copolymers near a Linear Selective Interface....Pages 129-154 Copolymers near a Random Selective Interface....Pages 155-179 Random Pinning and Wetting of Polymers....Pages 181-204 Polymers in a Random Potential....Pages 205-231 Back Matter....Pages 1-31