Directed Polymers in Random Environments: École d'Été de Probabilités de Saint-Flour XLVI – 2016: 2175 (Lecture Notes in Mathematics, 2175) - Softcover

Comets, Francis

Softcover

ISBN 10: 331950486X ISBN 13: 9783319504865

Publisher: Springer, 2017

Synopsis

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.

About this title

From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 2017
• ISBN 10: 331950486X
• ISBN 13: 9783319504865
• Binding: Paperback
• Language: English
• Edition number: 1
• Number of pages: 215