Related papers: Spatial Persistence of Fluctuating Interfaces
We consider a stochastic interface $h(x,t)$, described by the $1+1$ Kardar-Parisi-Zhang (KPZ) equation on the half-line $x\geq0$ with the reflecting boundary at $x=0$. The interface is initially flat, $h(x,t=0)=0$. We focus on the…
We show that the persistence probability $P(t,L)$, in a coarsening system of linear size $L$ at a time $t$, has the finite size scaling form $P(t,L)\sim L^{-z\theta}f(\frac{t}{L^{z}})$ where $\theta$ is the persistence exponent and $z$ is…
Height fluctuations of growing surfaces can be characterized by the probability distribution of height in a spatial point at a finite time. Recently there has been spectacular progress in the studies of this quantity for the…
The spatial distribution of unvisited/persistent sites in $d=1$ $A+A\to\emptyset$ model is studied numerically. Over length scales smaller than a cut-off $\xi(t)\sim t^{z}$, the set of unvisited sites is found to be a fractal. The fractal…
The surface tension of rough interfaces between coexisting phases in 2D and 3D Ising models are discussed in view of the known results and some original calculations presented in this paper. The results are summarised in a formula, which…
A pair of flat parallel surfaces, each freely diffusing along the direction of their separation, will eventually come into contact. If the shapes of these surfaces also fluctuate, then contact will occur when their centers of mass remain…
We study persistence in one-dimensional ferromagnetic and anti-ferromagnetic nearest-neighbor Ising models with parallel dynamics. The probability P(t) that a given spin has not flipped up to time t, when the system evolves from an initial…
We study the the survival probability P(t) upto time t, of a test particle moving in a fluctuating external field. The particle moves according to some prescribed deterministic or stochastic rules and survives as long as the external field…
We establish a thermodynamic limit and Gaussian fluctuations for the height and surface width of the random interface formed by the deposition of particles on surfaces. The results hold for the standard ballistic deposition model as well as…
The persistence exponent $\theta_o$ for the simple diffusion equation ${\phi}_t({\it x},t) = \triangle \phi (x,t)$ , with random Gaussian initial condition {\color{red},} has been calculated exactly using a method known as selective…
Consider the Ising model at low-temperatures and positive external field $\lambda$ on an $N\times N$ box with Dobrushin boundary conditions that are plus on the north, east, and west boundaries and minus on the south boundary. If $\lambda =…
The persistence of a stochastic variable is the probability that it does not cross a given level during a fixed time interval. Although persistence is a simple concept to understand, it is in general hard to calculate. Here we consider zero…
We study interface fluctuations for the $1$D stochastic Allen-Cahn equation perturbed by half a spatial derivative of the spacetime white noise. This half derivative makes the solution distribution-valued, so that proper renormalization is…
We obtain sharp asymptotics for the probability that the (2+1)-dimensional discrete SOS interface at low temperature is positive in a large region. For a square region $\Lambda$, both under the infinite volume measure and under the measure…
The persistence properties of a set of random walkers obeying the A+B -> 0 reaction, with equal initial density of particles and homogeneous initial conditions, is studied using two definitions of persistence. The probability, P(t), that an…
Persistence in coarsening 1D spin systems with a power law interaction $r^{-1-\sigma}$ is considered. Numerical studies indicate that for sufficiently large values of the interaction exponent $\sigma$ ($\sigma\geq 1/2$ in our simulations),…
Experimental realizations of a 1D interface always exhibit a finite microscopic width $\xi>0$; its influence is erased by thermal fluctuations at sufficiently high temperatures, but turns out to be a crucial ingredient for the description…
The effect of thermal fluctuations near a contact line of a liquid interface partially wetting an impenetrable substrate is studied analytically and numerically. Promoting both the interface profile and the contact line position to random…
We consider the limiting fluctuations of the geodesic in the directed landscape, conditioning on its length going to infinity. It was shown in \cite{Liu22b,Ganguly-Hegde-Zhang23} that when the directed landscape $\mathcal{L}(0,0;0,1) = L$…
We revisit the interface fluctuation problem for the $1$D Allen-Cahn equation perturbed by a small space-time white noise. We show that if the initial data is a standing wave solution to the deterministic equation, then under proper long…