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 Regional Energy Demand and Energy Efficiency in Japan by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book The Theory of Info-Dynamics: Rational Foundations of Information-Knowledge Dynamics by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Kazhdan-Lusztig Cells with Unequal Parameters by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Novel Methods and Technologies for Enterprise Information Systems by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Numerical Simulation of the Aerodynamics of High-Lift Configurations by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Adapting African Agriculture to Climate Change by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Chaperokine Activity of Heat Shock Proteins by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Kala Azar in South Asia by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Machine Learning, Optimization, and Big Data by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book The European Union as Guardian of Internet Privacy by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book International Medical Graduate Physicians by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Advances in Plant Dormancy by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Measuring Youth Well-being by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Advances in Design for Inclusion 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