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.
From the reviews: "This book provides an excellent introduction to the probabilistic studies of polymers. ... The main known results for each type of model are stated and explained in detail, accompanied by many short and self-contained proofs ... . At the end of each chapter, a list of extensions of the stated results is given, as well as a list of open problems. A bibliography is compiled at the end of the book, which includes many references to the physics as well as to the probability literature." (Rongfeng Sun, Mathematical Reviews, Issue 2010 h)