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.
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