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Directed Polymers in Random Environments

École d'Été de Probabilités de Saint-Flour XLVI – 2016

Francis Comets (Autor)

Buch | Softcover

XVI, 199 Seiten

2017 | 1st ed. 2017
Springer International Publishing (Verlag)
978-3-319-50486-5 (ISBN)

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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 questionis: 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 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 monographis aimed at researchers in probability or statistical physics, but is also accessible to masters and Ph.D. students.

1 Introduction.- 2 Thermodynamics and Phase Transition.- 3 The martingale approach and the L²region.- 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.

Erscheinungsdatum	19.02.2017
Reihe/Serie	École d'Été de Probabilités de Saint-Flour
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XVI, 199 p. 20 illus., 2 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Thermodynamik
Schlagworte	Kardar-Parisi-Zhang equation • Localization • Mathematics • mathematics and statistics • pinning transition • probability and statistics • Probability theory and stochastic processes • Random Media • random polymer models • Statistical Physics • Statistical Physics and Dynamical Systems • stochastics
ISBN-10	3-319-50486-X / 331950486X
ISBN-13	978-3-319-50486-5 / 9783319504865
Zustand	Neuware