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 Building Resilience of Human-Natural Systems of Pastoralism in the Developing World by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book PRICAI 2016: Trends in Artificial Intelligence by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Molecular Vaccines by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book PET/CT in Radiotherapy Planning by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Integrating the Participants’ Perspective in the Study of Language and Communication Disorders by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Nonlinear Dynamical Systems with Self-Excited and Hidden Attractors by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Periconception in Physiology and Medicine by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Operations Research and Enterprise Systems by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Fuzzy Sets-Based Methods and Techniques for Modern Analytics by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book A Critical Examination of Ethics in Health Care and Biomedical Research by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Indentation Testing of Biological Materials by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Vascular Disease in Older Adults by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Information Processing in Medical Imaging by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Multistate Analysis of Life Histories with R by Thomas Weiss, Patrik Ferrari, Herbert Spohn
Cover of the book Excel 2016 for Social Science Statistics 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