The Kardar-Parisi-Zhang equation and universality class

@article{Corwin2011TheKE,
title={The Kardar-Parisi-Zhang equation and universality class},
author={Ivan Corwin},
journal={arXiv: Probability},
year={2011}
}
• Ivan Corwin
• Published 8 June 2011
• Mathematics
• arXiv: Probability
Brownian motion is a continuum scaling limit for a wide class of random processes, and there has been great success in developing a theory for its properties (such as distribution functions or regularity) and expanding the breadth of its universality class. Over the past twenty five years a new universality class has emerged to describe a host of important physical and probabilistic models (including one dimensional interface growth processes, interacting particle systems and polymers in random…
292 Citations

Figures from this paper

Stochastic Analysis: Around the KPZ Universality Class
• Mathematics
• 2014
The Gaussian distribution is the "universal" distribution arising in a huge variety of contexts that describes the compound effect of the random fluctuations of many independent (or weakly dependent)
Growing interfaces uncover universal fluctuations behind scale invariance
• Physics
Scientific reports
• 2011
This work investigates growing interfaces of liquid-crystal turbulence and finds not only universal scaling, but universal distributions of interface positions, which obey the largest-eigenvalue distributions of random matrices and depend on whether the interface is curved or flat, albeit universal in each case.
Kardar-Parisi-Zhang universality of the Nagel-Schreckenberg model.
• Physics
Physical review. E
• 2019
The NaSch model also belongs to the KPZ class for general maximum velocities v_{max}>1, and the nonuniversal coefficients are calculated, fixing the exact asymptotic solutions for the dynamical structure function and the distribution of time-integrated currents.
Cutoff for the Glauber dynamics of the lattice free field
• Mathematics
• 2021
The Gaussian Free Field (GFF) is a canonical random surface in probability theory generalizing Brownian motion to higher dimensions, and is expected to be the universal scaling limit of a host of
Height distribution tails in the Kardar-Parisi-Zhang equation with Brownian initial conditions
• Mathematics
• 2017
For stationary interface growth, governed by the Kardar-Parisi-Zhang (KPZ) equation in 1 + 1 dimensions, typical fluctuations of the interface height at long times are described by the Baik-Rains
Kardar–Parisi–Zhang Universality
Universality in Random Systems Universality in complex random systems is a striking concept which has played a central role in the direction of research within probability, mathematical physics and
Kardar-Parisi-Zhang Equation and Universality
Polymer models belong to Kardar-Parisi-Zhang (KPZ) universality class, which is an extended family of models (kinetically roughened surfaces) which all share some non-Gaussian scaling limits and
Stirred Kardar-Parisi-Zhang Equation with Quenched Random Noise: Emergence of Induced Nonlinearity
• Physics
Universe
• 2022
We study the stochastic Kardar-Parisi-Zhang equation for kinetic roughening where the time-independent (columnar or spatially quenched) Gaussian random noise f(t,x) is specified by the pair
Nonstationary Generalized TASEP in KPZ and Jamming Regimes
• Physics
Journal of Statistical Physics
• 2021
We study the model of the totally asymmetric exclusion process with generalized update, which compared to the usual totally asymmetric exclusion process, has an additional parameter enhancing

References

SHOWING 1-10 OF 194 REFERENCES
Growing interfaces uncover universal fluctuations behind scale invariance
• Physics
Scientific reports
• 2011
This work investigates growing interfaces of liquid-crystal turbulence and finds not only universal scaling, but universal distributions of interface positions, which obey the largest-eigenvalue distributions of random matrices and depend on whether the interface is curved or flat, albeit universal in each case.
Stochastic Burgers and KPZ Equations from Particle Systems
• Mathematics
• 1997
Abstract: We consider two strictly related models: a solid on solid interface growth model and the weakly asymmetric exclusion process, both on the one dimensional lattice. It has been proven that,
Universality of slow decorrelation in KPZ growth
• Mathematics
• 2012
There has been much success in describing the limiting spatial fluctuations of growth models in the Kardar-Parisi-Zhang (KPZ) universality class. A proper rescaling of time should introduce a
Renormalization Fixed Point of the KPZ Universality Class
• Mathematics
• 2011
The one dimensional Kardar–Parisi–Zhang universality class is believed to describe many types of evolving interfaces which have the same characteristic scaling exponents. These exponents lead to a
Crossover distributions at the edge of the rarefaction fan
• Mathematics
• 2010
We consider the weakly asymmetric limit of simple exclusion process with drift to the left, starting from step Bernoulli initial data with $\rho_-<\rho_+$ so that macroscopically one has a
A pedestrian's view on interacting particle systems, KPZ universality, and random matrices
• Physics
• 2008
These notes are based on lectures delivered by the authors at a Langeoog seminar of SFB/TR12 "Symmetries and universality in mesoscopic systems" to a mixed audience of mathematicians and theoretical
Stochastic analysis on large scale interacting systems
• Mathematics
• 2004
Large deviations for the asymmetric simple exclusion process by S. R. S. Varadhan Random path representation and sharp correlations asymptotics at high temperatures by M. Campanino, D. Ioffe, and Y.
Large-distance and long-time properties of a randomly stirred fluid
• Mathematics
• 1977
Dynamic renormalization-group methods are used to study the large-distance, long-time behavior of velocity correlations generated by the Navier-Stokes equations for a randomly stirred, incompressible
Scaling Limits of Wick Ordered KPZ Equation
Abstract:Consider the KPZ equation , x∈ℝd, where W(t,x) is a space-time white noise. This paper investigates the question of whether, for some exponents χ and z, k{−χ}u(kzt, kx) converges in some
Scaling Limit for the Space-Time Covariance of the Stationary Totally Asymmetric Simple Exclusion Process
• Mathematics
• 2005
The totally asymmetric simple exclusion process (TASEP) on the one-dimensional lattice with the Bernoulli ρ measure as initial conditions, 0<ρ<1, is stationary in space and time. Let Nt(j) be the