Related papers: Spatial Persistence of Fluctuating Interfaces
Let a lattice gas of constant density, described by the symmetric simple exclusion process, be brought in contact with a "target": a spherical absorber of radius $R$. Employing the macroscopic fluctuation theory (MFT), we evaluate the…
We consider a model of first passage percolation (FPP) where the nearest-neighbor edges of the standard two-dimensional Euclidean lattice are equipped with random variables. These variables are i.i.d.\, nonnegative, continuous, and have a…
We study height fluctuations of interfaces in the $(1+1)$-dimensional Kardar-Parisi-Zhang (KPZ) class, growing at different speeds in the left half and the right half of space. Carrying out simulations of the discrete polynuclear growth…
In this study we try to answer the qustion : What happens when explicit constraints are introduced such that the low energy, long wavelength modes of a system are unavailable ? This question has assumed some importance in recent years due…
Consider the classical $(2+1)$-dimensional Solid-On-Solid model above a hard wall on an $L\times L$ box of $\bbZ^2$. The model describes a crystal surface by assigning a non-negative integer height $\eta_x$ to each site $x$ in the box and 0…
The height-height correlation function for a fluctuating interface between two coexisting bulk phases is derived by means of general equilibrium properties of the corresponding density-density correlation function. A wavelength-dependent…
We study fluctuations of polynomial linear statistics for discrete Schr\"odinger operators with a random decaying potential. We describe a decomposition of the space of polynomials into a direct sum of three subspaces determining the growth…
We investigate non-equilibrium fluctuations of a solid surface governed by the stochastic Mullins-Herring equation with conserved noise. This equation describes surface diffusion of adatoms accompanied by their exchange between the surface…
We studied numerically the validity of the fluctuation theorem, introduced by Evans,Cohen and Morris and proved by Gallavotti and Cohen, for a 2-dimensional system of particles maintained in a steady shear flow by Maxwell daemon boundary…
We consider the paths of a Gaussian random process $x(t)$, $x(0)=0$ not exceeding a fixed positive level over a large time interval $(0,T)$, $T\gg 1$. The probability $p(T)$ of such event is frequently a regularly varying function at…
We consider the asymptotic behavior of the KPZ fixed point $\{\mathsf H(x,t)\}_{x\in\mathbb R, t>0}$ conditioned on $\mathsf H(0,T)=L$ as $L$ goes to infinity. The main result is a conditional limit theorem for the fluctuations of $\mathsf…
Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…
In this paper we investigate the survival probability, \theta_n, in high-dimensional statistical physical models, where \theta_n denotes the probability that the model survives up to time n. We prove that if the r-point functions scale to…
A numerical study of the transfer across random fractal surfaces shows that their responses are very close to the response of deterministic model geometries with the same fractal dimension. The simulations of several interfaces with…
We discuss aspects of the problem of assigning probabilities in eternal inflation. In particular, we investigate a recent suggestion that the lowest energy de Sitter vacuum in the landscape is effectively stable. The associated proposal for…
We propose a method to describe the short-distance behavior of an interface fluctuating in the presence of the wedge-shaped substrate near the critical filling transition. Two different length scales determined by the average height of the…
We reconsider the problem of local persistence in directed site percolation. We present improved estimates of the persistence exponent in all dimensions from 1+1 to 7+1, obtained by new algorithms and by improved implementations of existing…
We investigate the fluctuation of the top location of a sandpile numerically using the two-dimensional discrete elements method. We feed particles to a sandpile at a fixed time interval and calculate power spectra from the time series of…
We consider a model of interface growth in two dimensions, given by a height function on the sites of the one--dimensional integer lattice. According to the discrete time update rule, the height above the site $x$ increases to the height…
We discuss the transient and steady state fluctuation relation for a mechanical system in contact with two deterministic thermostats at different temperatures. The system is a modified Lorentz gas in which the fixed scatterers exchange…