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 Metal Impurities in Silicon- and Germanium-Based Technologies by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Artificial Intelligence Techniques for Rational Decision Making by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Infostorms by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Towards Global Sustainability by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Judicial Activism by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Potential Game Theory by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Physical Play and Children’s Digital Games by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book American Presidential Statecraft by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book American Presidential Statecraft by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Extracellular Potentials in the Hippocampus by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Complex Systems and Social Practices in Energy Transitions by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Land-Cover and Land-Use Changes in Eastern Europe after the Collapse of the Soviet Union in 1991 by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book The Vascular Flora of the National Park of Abruzzo, Lazio and Molise (Central Italy) by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Korean Women, Self-Esteem, and Practical Theology by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Targeting Autophagy in Cancer Therapy 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