ENGLISH

Reflected Brownian Motions in the KPZ Universality Class

By Thomas Weiss , Patrik Ferrari , Herbert Spohn (auth.)

Book information

Publisher
Springer International Publishing
Year
2017
ISBN
978-3-319-49498-2, 978-3-319-49499-9
DOI
10.1007/978-3-319-49499-9
Language
english
Format
PDF
Filesize
2 MB (1840592 bytes)
Series
SpringerBriefs in Mathematical Physics 18
Edition
1
Pages
VII, 118\121
Time added
2017-02-20 14:56:08
Statistical Physics and Dynamical Systems;Mathemat

Description

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.

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