# The Kardar-Parisi-Zhang Equation and Universality Class

@inproceedings{KARDARPARISIZHANG2011TheKE, title={The Kardar-Parisi-Zhang Equation and Universality Class}, author={The KARDAR-PARISI-ZHANG}, 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…

## 359 Citations

Time evolution of the Kardar-Parisi-Zhang equation

- Mathematics
- 2020

The use of the non-linear SPDEs are inevitable in both physics and applied mathematics since many of the physical phenomena in nature can be effectively modeled in random and non-linear way. The…

Anomalous ballistic scaling in the tensionless or inviscid Kardar-Parisi-Zhang equation

- Physics
- 2022

The one-dimensional Kardar-Parisi-Zhang (KPZ) equation is becoming an overarching paradigm for the scaling of nonequilibrium, spatially extended, classical and quantum systems with strong…

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 Fluctuations for the Stationary KPZ Equation

- Mathematics
- 2014

We compute the one-point probability distribution for the stationary KPZ equation (i.e. initial data H(0,X)=B(X)$\mathcal {H}(0,X)=B(X)$, for B(X) a two-sided standard Brownian motion) and show that…

Hydrodynamic limit and viscosity solutions for a 2D growth process in the anisotropic KPZ class

- Mathematics
- 2017

We study a $(2+1)$-dimensional stochastic interface growth model, that is believed to belong to the so-called Anisotropic KPZ (AKPZ) universality class [Borodin and Ferrari, 2014]. It can be seen…

The KPZ Equation, Non-Stationary Solutions, and Weak Universality for Finite-Range Interactions

- Mathematics
- 2018

We study the weak KPZ universality problem by extending the KPZ universality results for weakly asymmetric exclusion processes to non-simple variants under deterministic initial data with constant…

Evidence for Geometry-Dependent Universal Fluctuations of the Kardar-Parisi-Zhang Interfaces in Liquid-Crystal Turbulence

- Physics
- 2012

We provide a comprehensive report on scale-invariant fluctuations of growing interfaces in liquid-crystal turbulence, for which we recently found evidence that they belong to the Kardar-Parisi-Zhang…

KPZ and Airy limits of Hall-Littlewood random plane partitions

- Mathematics
- 2016

In this paper we consider a probability distribution on plane partitions, which arises as a one-parameter generalization of the q^{volume} measure. This generalization is closely related to the…

The endpoint distribution of directed polymers

- Mathematics
- 2016

Probabilistic models of directed polymers in random environment have received considerable attention in recent years. Much of this attention has focused on integrable models. In this paper, we…

Intermittency of the Malliavin Derivatives and Regularity of the Densities for a Stochastic Heat Equation

- Mathematics
- 2012

Author(s): Mahboubi, Pejman | Advisor(s): Liggett, Thomas | Abstract: In recent decades, as a result of mathematicians' endeavor to come up with more realistic models for complex phenomena, the…

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