Related papers: How flat is flat in random interface growth?
The Kardar-Parisi-Zhang (KPZ) universality class describes the coarse-grained behavior of a wealth of classical stochastic models. Surprisingly, it was recently conjectured to also describe spin transport in the one-dimensional quantum…
The Kardar-Parisi-Zhang (KPZ) equation sets the universality class for growing and roughening of nonequilibrium surfaces without any conservation law and nonlocal effects. We argue here that the KPZ equation can be generalized by including…
We study discrete KPZ growth models deposited on square lattice substrates, whose (average) lateral size enlarges as $L= L_0 + \omega t^{\gamma}$. Our numerical simulations reveal that the competition between the substrate expansion and the…
We define a stochastic lattice model for a fluctuating directed polymer in $d\geq 2$ dimensions. This model can be alternatively interpreted as a fluctuating random path in 2 dimensions, or a one-dimensional asymmetric simple exclusion…
We consider the stochastic six-vertex (S6V) model and asymmetric simple exclusion process (ASEP) under general initial conditions which are bounded below lines of arbitrary slope at $\pm\infty$. We show under Kardar-Parisi-Zhang (KPZ)…
The time-dependent probability distribution function of the height for the Kardar-Parisi-Zhang equation with sharp wedge initial conditions has been obtained recently as a convolution between the Gumbel distribution and a difference of two…
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…
Fredholm determinants associated to deformations of the Airy kernel are closely connected to the solution to the Kardar-Parisi-Zhang (KPZ) equation with narrow wedge initial data, and they also appear as largest particle distribution in…
A Cauchy-characteristic initial value problem for the Einstein-Klein-Gordon system with spherical symmetry is presented. Initial data are specified on the union of a space-like and null hypersurface. The development of the data is obtained…
The relaxation time limit of the one-point distribution of the spatially periodic totally asymmetric simple exclusion process is expected to be the universal one point distribution for the models in the KPZ universality class in a periodic…
We continue to study a model of disordered interface growth in two dimensions. The interface is given by a height function on the sites of the one--dimensional integer lattice and grows in discrete time: (1) the height above the site $x$…
We study the half-space KPZ equation with a Neumann boundary condition, starting from stationary Brownian initial data. We derive a variance identity that links the fluctuations of the height function to the transversal fluctuations of a…
We study the probability distribution $\mathcal{P}(H,t,L)$ of the surface height $h(x=0,t)=H$ in the Kardar-Parisi-Zhang (KPZ) equation in $1+1$ dimension when starting from a parabolic interface, $h(x,t=0)=x^2/L$. The limits of…
We have characterized the scaling behavior of the first-passage percolation (FPP) model on two types of discrete networks, the regular square lattice and the disordered Delaunay lattice, thereby addressing the effect of the underlying…
We report numerical and analytic results for the spatial survival probability for fluctuating one-dimensional interfaces with Edwards-Wilkinson or Kardar-Parisi-Zhang dynamics in the steady state. Our numerical results are obtained from…
Stochastic interface dynamics serve as mathematical models for diverse time-dependent physical phenomena: the evolution of boundaries between thermodynamic phases, crystal growth, random deposition... Interesting limits arise at large…
We describe a directed avalanche model; a slowly unloading sandbox driven by lowering a retaining wall. The directness of the dynamics allows us to interpret the stable sand surfaces as world sheets of fluctuating interfaces in one lower…
In this paper we consider two models in the Kardar-Parisi-Zhang (KPZ) universality class, the asymmetric simple exclusion process (ASEP) and the stochastic six-vertex model. We introduce a new class of initial data (which we call {\itshape…
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…
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…