Related papers: Kardar-Parisi-Zhang Equation from Long-Range Exclu…
Large scale, dynamical simulations have been performed for the two dimensional octahedron model, describing the Kardar-Parisi-Zhang (KPZ) for nonlinear, or the Edwards-Wilkinson (EW) class for linear surface growth. The autocorrelation…
We consider the colored asymmetric simple exclusion process (ASEP) and stochastic six vertex (S6V) model with fully packed initial conditions; the states of these models can be encoded by 2-parameter height functions. We show under…
In discrete models describing growing rough interfaces of the Kardar-Parisi-Zhang universality class, we examine height fluctuations at a fixed site as a function of time in the monolayer unit. For small systems, we show that it is possible…
We obtain several exact results for universal distributions involving the maximum of the Airy$_2$ process minus a parabola and plus a Brownian motion, with applications to the 1D Kardar-Parisi-Zhang (KPZ) stochastic growth universality…
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 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 clustering of particles. We derive the exact…
Over the past years our understanding of the scaling properties of the solutions to the one-dimensional KPZ equation has advanced considerably, both theoretically and experimentally. In our contribution we export these insights to the case…
We analyze the one-dimensional periodic Kardar-Parisi-Zhang equation in the language of paracontrolled distributions, giving an alternative viewpoint on the seminal results of Hairer. Apart from deriving a basic existence and uniqueness…
We consider the scaling limits for a one-dimensional random growth model, the weakly asymmetric single step Solid-on-Solid process. We show that the fluctuation field, if considered in an appropriate (long) space-time scale, solves the…
We consider generalizations of open ASEP in the interval and half-space, where the speed of the reservoir dynamics can depend on the local particle configuration. We show that their height functions have a continuum limit given by the open…
Inspired by the recent results on totally asymmetric simple exclusion processes on a periodic lattice with short-ranged quenched hopping rates [A. Haldar, A. Basu, Phys Rev Research 2, 043073 (2020)], we study the universal scaling…
We investigate the Kardar--Parisi--Zhang (KPZ) equation in $d$ spatial dimensions with Gaussian spatially long--range correlated noise --- characterized by its second moment $R(\vec{x}-\vec{x}') \propto |\vec{x}-\vec{x}'|^{2\rho-d}$ --- by…
In this paper, we introduce a novel integration method of Kardar-Parisi-Zhang (KPZ) equation. It has always been known that if during the discrete integration of the KPZ equation the nearest-neighbor height-difference exceeds a critical…
We study the interface dynamics of a discrete model to quantitatively describe electrochemical deposition experiments. Extensive numerical simulations indicate that the interface dynamics is unstable at early times, but asymptotically…
Growth of interfaces during vapor deposition are analyzed on a discrete lattice. Foe a rough surface, relation between the roughness exponent alpha, and corresponding step-step (slope-slope) couplings is obtained in (1+1) and (2+1)…
The one-point distribution of the height for the continuum Kardar-Parisi-Zhang (KPZ) equation is determined numerically using the mapping to the directed polymer in a random potential at high temperature. Using an importance sampling…
We consider the Kardar-Parisi-Zhang (KPZ) equation for a circular interface in two dimensions, unconstrained by the standard small-slopes and no-overhang approximations. Numerical simulations using an adaptive scheme allow us to elucidate…
Barraquand and Le~Doussal introduced a family of stationary measures for the (conjectural) KPZ fixed point on an interval with Neumann boundary conditions, and predicted that they arise as scaling limit of stationary measures of all models…
In this paper we discuss the well known Kardar Parisi Zhang (KPZ) equation driven by temporally correlated noise. We use a self consistent approach to derive the scaling exponents of this system. We also draw general conclusions about the…
The Kardar-Parisi-Zhang (KPZ) equation of nonlinear stochastic growth in d dimensions is studied using the mapping onto a system of directed polymers in a quenched random medium. The polymer problem is renormalized exactly in a minimally…