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Record Nr. |
UNISALENTO991003392369707536 |
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Autore |
Comets, Francis |
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Titolo |
Directed polymers in random environments [e-book] : École d'Été de Probabilités de Saint-Flour XLVI-2016 / Francis Comets |
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Pubbl/distr/stampa |
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ISBN |
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Descrizione fisica |
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Collana |
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Lecture notes in mathematics, 1617-9692 ; 2175 |
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Classificazione |
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AMS 60K37 |
AMS 60F10 |
AMS 60H05 |
AMS 60J10 |
AMS 82-01 |
AMS 82B20 |
AMS 82B41 |
AMS 82D60 |
LC QA274.73 |
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Altri autori (Convegni) |
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Ecole d'été de probabilités de Saint-Flour <46. ; 2016 ; Saint-Flour, France> |
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Disciplina |
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Soggetti |
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Random walks (Mathematics) |
Martingales (Mathematics) |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index |
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Nota di contenuto |
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1 Introduction ; 2 Thermodynamics and Phase Transition ; 3 The martingale approach and the L2 region ; 4 Lattice versus tree ; 5 Semimartingale approach and localization transition ; 6 Log-Gamma polymer model ; 7 Kardar-Parisi-Zhang equation and universality ; 8 Variational formulas. |
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Sommario/riassunto |
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Analyzing the phase transition from diffusive to localized behavior in a model of directed polymers in a random environment, this volume places particular emphasis on the localization phenomenon. The main question is: What does the path of a random walk look like if rewards and penalties are spatially randomly distributed? This model, which provides a simplified version of stretched elastic chains pinned by random impurities, has attracted much research activity, but it (and its relatives) still holds many secrets, especially in high dimensions. It has |
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non-gaussian scaling limits and it belongs to the so-called KPZ universality class when the space is one-dimensional. Adopting a Gibbsian approach, using general and powerful tools from probability theory, the discrete model is studied in full generality. Presenting the state-of-the art from different perspectives, and written in the form of a first course on the subject, this monograph is aimed at researchers in probability or statistical physics, but is also accessible to masters and Ph.D. students |
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