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Reflected Brownian motions in the KPZ universality class

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Reflected Brownian motions in the KPZ universality class/ by Thomas Weiss, Patrik Ferrari, Herbert Spohn.
Author:	Weiss, Thomas.
other author:	Ferrari, Patrik.
Published:	Cham :Springer International Publishing : : 2017.,
Description:	vii, 118 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Brownian motion processes. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-49499-9
ISBN:	9783319494999

Reflected Brownian motions in the KPZ universality class
Weiss, Thomas.

Reflected Brownian motions in the KPZ universality class[electronic resource] /by Thomas Weiss, Patrik Ferrari, Herbert Spohn. - Cham :Springer International Publishing :2017. - vii, 118 p. :ill., digital ;24 cm. - SpringerBriefs in mathematical physics,v.182197-1757 ;. - SpringerBriefs in mathematical physics ;v.2..

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.

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.

ISBN: 9783319494999

Standard No.: 10.1007/978-3-319-49499-9doiSubjects--Topical Terms:

672027
Brownian motion processes.

LC Class. No.: QA274.75

Dewey Class. No.: 519.233

Reflected Brownian motions in the KPZ universality class
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245 1 0 $a Reflected Brownian motions in the KPZ universality class $h [electronic resource] / $c by Thomas Weiss, Patrik Ferrari, Herbert Spohn.
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300 $a vii, 118 p. : $b ill., digital ; $c 24 cm.
490 1 $a SpringerBriefs in mathematical physics, $x 2197-1757 ; $v v.18
505 0 $a 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.
520 $a 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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650 2 4 $a Mathematical Physics. $3 786661
650 2 4 $a Probability Theory and Stochastic Processes. $3 593945
700 1 $a Ferrari, Patrik. $3 1249940
700 1 $a Spohn, Herbert. $3 685521
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