• Corpus ID: 251320277

An invariance principle for the 1D KPZ equation

  title={An invariance principle for the 1D KPZ equation},
  author={Arka Adhikari and Sourav Chatterjee},
A BSTRACT . Consider a discrete one-dimensional random surface whose height at a point grows as a function of the heights at neighboring points plus an independent random noise. Assuming that this function is equivariant under constant shifts, symmetric in its arguments, and at least six times continuously differentiable in a neighborhood of the origin, we show that as the variance of the noise goes to zero, any such process converges to the Cole–Hopf solution of the 1D KPZ equation under a… 



A central limit theorem for the KPZ equation

We consider the KPZ equation in one space dimension driven by a stationary centred space-time random field, which is sufficiently integrable and mixing, but not necessarily Gaussian. We show that, in

Universality of deterministic KPZ

Consider a deterministically growing surface of any dimension, where the growth at a point is an arbitrary nonlinear function of the heights at that point and its neighboring points. Assuming that

Integrable fluctuations in the KPZ universality class

A BSTRACT . The KPZ fixed point is a scaling invariant Markov process which arises as the universal scaling limit of a broad class of models of random interface growth in one dimension, the

The 1  +  1 dimensional Kardar–Parisi–Zhang equation: more surprises

  • H. Spohn
  • Physics
    Journal of Statistical Mechanics: Theory and Experiment
  • 2020
In its original version, the KPZ equation models the dynamics of an interface bordering a stable phase against a metastable one. Over the past few years the corresponding two-dimensional field theory

Local KPZ behavior under arbitrary scaling limits

One of the main difficulties in proving convergence of discrete models of surface growth to the Kardar–Parisi–Zhang (KPZ) equation in dimensions higher than one is that the correct way to take a

KPZ equation, its renormalization and invariant measures

The Kardar–Parisi–Zhang (KPZ) equation is a stochastic partial differential equation which is ill-posed because of the inconsistency between the nonlinearity and the roughness of the forcing noise.

Space–Time Discrete KPZ Equation

A general family of space–time discretizations of the KPZ equation are studied and it is shown that they converge to its solution.

Solving the KPZ equation

We introduce a new concept of solution to the KPZ equation which is shown to extend the classical Cole-Hopf solution. This notion provides a factorisation of the Cole-Hopf solution map into a

The Kardar–Parisi–Zhang Equation as Scaling Limit of Weakly Asymmetric Interacting Brownian Motions

We consider a system of infinitely many interacting Brownian motions that models the height of a one-dimensional interface between two bulk phases. We prove that the large scale fluctuations of the

The Continuum Directed Random Polymer

Motivated by discrete directed polymers in one space and one time dimension, we construct a continuum directed random polymer that is modeled by a continuous path interacting with a space-time white