# 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} }

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

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

- PhysicsScientific 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.

- PhysicsPhysical 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

- Mathematics
- 2016

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

- Physics
- 2017

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

- PhysicsUniverse
- 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

- PhysicsJournal 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

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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…

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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…

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