Random polymers: Ecole d'été de probabilités de Saint-Flour XXXVII-2007 / Frank den Hollander

Collectivité principale: école d'été de probabilités de Saint-Flour, 37, Saint-Flour (2007) Co-auteur: Den Hollander, Frank (1956-) - AuteurType de document: CongrèsCollection: Lecture notes in mathematics, école d'été de probabilités de Saint-Flour ; 1974Langue: anglaisPays: AllemagneÉditeur: Berlin : Springer, 2009Description: 1 vol. (XIII-258 p.) : fig. ; 24 cm ISBN: 9783642003325 ; br. ISSN: 0075-8434Résumé: 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. (Source : 4ème de couverture).Bibliographie: Bibliogr. p. 233-247. Index. Sujets MSC: 82-02 Statistical mechanics, structure of matter -- Research exposition (monographs, survey articles)
60K35 Probability theory and stochastic processes -- Special processes -- Interacting random processes; statistical mechanics type models; percolation theory
60F10 Probability theory and stochastic processes -- Limit theorems -- Large deviations
60K37 Probability theory and stochastic processes -- Special processes -- Processes in random environments
82B26 Statistical mechanics, structure of matter -- Equilibrium statistical mechanics -- Phase transitions (general)
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Bibliogr. p. 233-247. Index

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. (Source : 4ème de couverture)

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