Reflected Brownian Motions in the KPZ Universality Class

Nonfiction, Science & Nature, Science, Physics, Mathematical Physics, Mathematics, Statistics
Cover of the book Reflected Brownian Motions in the KPZ Universality Class by Thomas Weiss, Patrik Ferrari, Herbert Spohn, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Thomas Weiss, Patrik Ferrari, Herbert Spohn ISBN: 9783319494999
Publisher: Springer International Publishing Publication: December 16, 2016
Imprint: Springer Language: English
Author: Thomas Weiss, Patrik Ferrari, Herbert Spohn
ISBN: 9783319494999
Publisher: Springer International Publishing
Publication: December 16, 2016
Imprint: Springer
Language: English

This book presents a detailed study of a system of interacting Brownian motions in one dimension. The interaction is point-like such that the n-th Brownian motion is reflected from the Brownian motion with label n-1. This model belongs to the Kardar-Parisi-Zhang (KPZ) universality class. In fact, because of the singular interaction, many universal properties can be established with rigor. They depend on the choice of initial conditions. Discussion addresses packed and periodic initial conditions (Chapter 5), stationary initial conditions (Chapter 6), and mixtures thereof (Chapter 7). The suitably scaled spatial process will be proven to converge to an Airy process in the long time limit. A chapter on determinantal random fields and another one on Airy processes are added to have the notes self-contained. These notes serve as an introduction to the KPZ universality class, illustrating the main concepts by means of a single model only. The notes will be of interest to readers from interacting diffusion processes and non-equilibrium statistical mechanics.

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

This book presents a detailed study of a system of interacting Brownian motions in one dimension. The interaction is point-like such that the n-th Brownian motion is reflected from the Brownian motion with label n-1. This model belongs to the Kardar-Parisi-Zhang (KPZ) universality class. In fact, because of the singular interaction, many universal properties can be established with rigor. They depend on the choice of initial conditions. Discussion addresses packed and periodic initial conditions (Chapter 5), stationary initial conditions (Chapter 6), and mixtures thereof (Chapter 7). The suitably scaled spatial process will be proven to converge to an Airy process in the long time limit. A chapter on determinantal random fields and another one on Airy processes are added to have the notes self-contained. These notes serve as an introduction to the KPZ universality class, illustrating the main concepts by means of a single model only. The notes will be of interest to readers from interacting diffusion processes and non-equilibrium statistical mechanics.

More books from Springer International Publishing

Cover of the book Challenges in Health and Development by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Reassessing the Role of Management in the Golden Age by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Web-Age Information Management by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Natural Resources Available Today and in the Future by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Ubiquitous Networking by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Computer Aided Verification by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Knowledge Engineering and Semantic Web by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book The Influence of Human Rights and Basic Rights in Private Law by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Violence in Nigeria by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book A Sustainable Bioeconomy by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Rural Welfare in China by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Debating Collaboration and Complicity in War Crimes Trials in Asia, 1945-1956 by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Assessment and Intervention for English Language Learners by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Artificial Intelligence and Security by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Implant Aesthetics by Thomas Weiss, Patrik Ferrari, Herbert Spohn
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy