Related papers: Exactly solving the KPZ equation
We consider the fluctuations in the stochastic growth of a one-dimensional interface of height $h(x,t)$ described by the Kardar-Parisi-Zhang (KPZ) universality class. We study the joint probability distribution function (JPDF) of the…
We study atypically large fluctuations of height $H$ in the 1+1-dimensional Kardar-Parisi-Zhang (KPZ) equation at long times $t$, when starting from a "droplet" initial condition. We derive exact large deviation function of height for…
{\em NOTE: This paper presented the first attempt to tackle the Kardar-Parisi-Zhang (KPZ) equation using non-perturbative renormalisation group (NPRG) methods. It exploited the most natural and frequently used approximation scheme within…
Our understanding of the one-dimensional KPZ equation, \textit{alias} noisy Burgers equation, has advanced substantially over the past five years. We provide a non-technical review, where we limit ourselves to the stochastic PDE and lattice…
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 correlations. Recent analytical solutions have…
We consider an infinite interface in $d>2$ dimensions, governed by the Kardar-Parisi-Zhang (KPZ) equation with a weak Gaussian noise which is delta-correlated in time and has short-range spatial correlations. We study the probability…
Kardar-Parisi-Zhang (KPZ) equation is a quasilinear stochastic partial differential equation(SPDE) driven by a space-time white noise. In recent years there have been several works directed towards giving a rigorous meaning to a solution of…
Using the weak-noise theory, we evaluate the probability distribution $\mathcal{P}(H,t)$ of large deviations of height $H$ of the evolving surface height $h(x,t)$ in the Kardar-Parisi-Zhang (KPZ) equation in one dimension when starting from…
In order to perform numerical simulations of the KPZ equation, in any dimensionality, a spatial discretization scheme must be prescribed. The known fact that the KPZ equation can be obtained as a result of a Hopf--Cole transformation…
We present a series of recent results on the well-posedness of very singular parabolic stochastic partial differential equations. These equations are such that the question of what it even means to be a solution is highly non-trivial. This…
We consider the one-dimensional Kardar-Parisi-Zhang (KPZ) equation with half Brownian motion initial condition, studied previously through the weakly asymmetric simple exclusion process. We employ the replica Bethe ansatz and show that the…
In this short communication we show that basic tools from Malliavin calculus can be applied to derive the two-point function of the slope of the one-dimensional KPZ equation, starting from an arbitrary two-sided Brownian motion, in terms of…
The article covers the one-dimensional Kardar-Parisi-Zhang equation, weak drive limit, universality, directed polymers in a random medium, replica solutions, statistical mechanics of line ensembles, and its generalization to several…
We benchmark the ZPC parton cascade with an exact analytical solution of the relativistic Boltzmann equation for a homogeneous and massless gas with a constant and isotropic elastic cross section. We measure the accuracy of ZPC with the…
This paper concerns the multi-component coupled Kardar-Parisi-Zhang (KPZ) equation and its two types of approximations. One approximation is obtained as a simple replacement of the noise term by a smeared noise with a proper…
We consider a large class of $1+1$-dimensional continuous interface growth models and we show that, in both the weakly asymmetric and the intermediate disorder regimes, these models converge to Hopf-Cole solutions to the KPZ equation.
We study the complete probability distribution $\mathcal{P}\left(\bar{H},t\right)$ of the time-averaged height $\bar{H}=(1/t)\int_0^t h(x=0,t')\,dt'$ at point $x=0$ of an evolving 1+1 dimensional Kardar-Parisi-Zhang (KPZ) interface…
A novel algorithm is envisaged to extract the coupling parameters of the Kardar-Parisi-Zhang (KPZ) equation from experimental data. The method hinges on the Fokker-Planck equation combined with a classical least-square error procedure. It…
We study the long-time regime of the Kardar-Parisi-Zhang (KPZ) equation in $1+1$ dimensions for the Brownian and droplet initial conditions and present a simple derivation of the tail of the large deviations of the height on the negative…
It was recently proved in [Corwin-Shen, 2016] that under weak asymmetry scaling, the height functions for open ASEP on the half-line and on a bounded interval converge to the Hopf-Cole solution of the KPZ equation with Neumann boundary…