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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Reflected Brownian Motions in the Kpz Universality Class

Reflected Brownian Motions in the Kpz Universality Class

Weiss, Thomas
Ferrari, Patrik
Spohn, Herbert

Paperback

Series: Springerbriefs in Mathematical Physics, Book 18

PhysicsProbability & Statistics

ISBN10: 3319494988
ISBN13: 9783319494982
Publisher: Springer
Published: Dec 28 2016
Pages: 118
Weight: 0.42
Height: 0.27 Width: 6.14 Depth: 9.21
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 modelonly. The notes will be of interest to readers from interacting diffusion processes and non-equilibrium statistical mechanics.

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