Directed Polymers in Random Environments

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Beschreibung

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 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.

is: What does the path of a random walk look like if rewards and penalties are spatially randomly distributed?

Zusammenfassung

The first book to be devoted to this active field of research in probability and statistical physics

Aimed at experienced researchers, but also accessible to masters and Ph.D. students

Authored by a leading expert in the subject

Includes supplementary material: [...]

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2017
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Lecture Notes in Mathematics
Inhalt:	xvi 199 S. 18 s/w Illustr. 2 farbige Illustr. 199 p. 20 illus. 2 illus. in color.
ISBN-13:	9783319504865
ISBN-10:	331950486X
Sprache:	Englisch
Herstellernummer:	978-3-319-50486-5
Einband:	Kartoniert / Broschiert
Autor:	Comets, Francis
Auflage:	1st edition 2017
Hersteller:	Springer Springer International Publishing AG Lecture Notes in Mathematics
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 13 mm
Von/Mit:	Francis Comets
Erscheinungsdatum:	01.02.2017
Gewicht:	0,341 kg