Reflected Brownian motions in the KPZ universality class / Thomas Weiss, Patrik Ferrari, Herbert Spohn.
Weiss, Thomas, author.; Ferrari, Patrik, author.; Spohn, Herbert, author.
2017
QA274.75
Available Online

Linked e-resources

Linked Resource
Online Access
Concurrent users
Unlimited
Authorized users
Authorized users
Document Delivery Supplied
Can lend chapters, not whole ebooks

Details

Title
Reflected Brownian motions in the KPZ universality class / Thomas Weiss, Patrik Ferrari, Herbert Spohn.
Author
Weiss, Thomas, author.
ISBN
9783319494999 (electronic book)
3319494996 (electronic book)
9783319494982
3319494988
DOI
https://doi.org/10.1007/978-3-319-49499-9
Published
Cham, Switzerland : Springer, 2017.
Language
English
Description
1 online resource.
Item Number
10.1007/978-3-319-49499-9 doi
Call Number
QA274.75
Dewey Decimal Classification
519.2/33
Summary
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.
Access Note
Access limited to authorized users.
Digital File Characteristics
text file PDF
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed December 22, 2016).
Added Author
Ferrari, Patrik, author.
Spohn, Herbert, author.
Series
SpringerBriefs in mathematical physics ; v. 18.
Available in Other Form
Print version: 9783319494982
Linked Resources
Online Access
Record Appears in
Online Resources > Ebooks
All Resources
Introduction
One-sided reflected Brownian motions and related models
Skorokhod construction
Packed initial conditions
Infinite particle systems
Determinantal point processes
Definition
Fredholm determinants
Correlation kernel
Strategy for future proofs.-Airy processes.-Elementary Airy processes
Crossover Processes
Variational identities
Gaussian fluctuations of the Airy_stat process
Packed and Periodic initial conditions
Packed initial conditions
Periodic initial conditions
Stationary initial conditions
Poisson initial conditions
Determinantal structure
Asymptotic analysis
Path-integral style formula
Analytic continuation
More general initial conditions and their asymptotics
Half-Periodic initial conditions
Half-Poisson initial conditions
Poisson-Periodic initial conditions
Attractiveness and a more general class of initial data
Asymptotics along space-like paths and slow decorrelations
References.

Browse Subjects

Show more subjects...

Statistics

from
to
Export