Reflected Brownian Motions in the KPZ Universality Class
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Beschreibung
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 modelonly. The notes will be of interest to readers from interacting diffusion processes and non-equilibrium statistical mechanics.
Includes supplementary material: sn.pub/extras
Autor*in
Thomas Weiss
Themen in »Reflected Brownian Motions in the KPZ Universality Class«
Kardar-Parisi-Zhang equation stochastic PDE Bethe Ansatz Skorokhod construction last passage percolation determinantal point process Fredholm determinants Eynard-Metha Theorem determinantal structure Poisson initial conditions Airy proceses steepest descent contour integration polynuclear growth model TASEP model