Directed Polymers in Random Environments
École d'Été de Probabilités de Saint-Flour XLVI - 2016
Published on 26. January 2017
XVI, 199 pages
978-3-319-50487-2 (ISBN)
Description
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.
More details
Series
Edition
1st ed. 2017
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Product notice
Reflowable
Illustrations
XVI, 199 p. 20 illus., 2 illus. in color.
File size
3,17 MB
ISBN-13
978-3-319-50487-2 (9783319504872)
DOI
10.1007/978-3-319-50487-2
Schweitzer Classification
Other editions
Additional editions
Francis Comets
Directed Polymers in Random Environments
École d'Été de Probabilités de Saint-Flour XLVI - 2016
Book
02/2017
Springer
€40.65
Shipment within 10-15 days
Content
1 Introduction.- 2 Thermodynamics and Phase Transition.- 3 The martingale approach and the
L
2
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.
