Directed Polymers in Random Environments

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

Nonfiction, Science & Nature, Science, Physics, Mathematical Physics, Mathematics, Statistics
Cover of the book Directed Polymers in Random Environments by Francis Comets, Springer International Publishing
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Author: Francis Comets ISBN: 9783319504872
Publisher: Springer International Publishing Publication: January 26, 2017
Imprint: Springer Language: English
Author: Francis Comets
ISBN: 9783319504872
Publisher: Springer International Publishing
Publication: January 26, 2017
Imprint: Springer
Language: English

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

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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

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