Related papers: Dynamic scaling in the spatial distribution of per…
A study of persistence dynamics is made for the first time in a quantum system by considering the dynamics of a quantum random walk. For a discrete walk on a line starting at $x=0$ at time $t=0$, the persistence probability $P(x,t)$ that a…
In this paper we address the one-dimensional problem of stochastic renewal in different damping environments. An ensemble of particles with some specified initial distribution in phase space are allowed to evolve stochastically till a…
We extend a previously proposed deposition model with two kinds of particles, considering the restricted solid-on-solid condition. The probability of incidence of particle C (A) is p (1-p). Aggregation is possible if the top of the column…
The fraction r(t) of spins which have never flipped up to time t is studied within a linear diffusion approximation to phase ordering. Numerical simulations show that, even in this simple context, r(t) decays with time like a power-law with…
We investigate the statistics of the number $N(R,S)$ of lattice points, $n\in \Z^2$, in a ``random'' annular domain $\Pi(R,w)=\,(R+w)A\,\setminus RA$, where $R,w >0$. Here $A$ is a fixed convex set with smooth boundary and $w$ is chosen so…
We consider one-dimensional discrete-time random walks (RWs) of $n$ steps, starting from $x_0=0$, with arbitrary symmetric and continuous jump distributions $f(\eta)$, including the important case of L\'evy flights. We study the statistics…
We have considered the persistence of unvisited sites of a lattice, i.e., the probability $S(t)$ that a site remains unvisited till time $t$ in presence of mutually repulsive random walkers. The dynamics of this system has direct…
A one dimensional $A+A \to \emptyset$ system where the direction of motion of the particles is determined by the position of the nearest neighours is studied. The particles move with a probability $0.5 + \epsi$ towards their nearest…
We investigate statistics of dynamical exchange events in coarse--grained models of supercooled liquids in spatial dimensions $d=1$, 2, and 3. The models, based upon the concept of dynamical facilitation, capture generic features of…
We introduce a generalized homogeneous function to describe the joint probability density for magnitude and duration of events in self-organized critical systems (SOC). It follows that the cumulative distributions of magnitude and of…
Let $\tau = (\tau_i : i \in {\Bbb Z})$ denote i.i.d.~positive random variables with common distribution $F$ and (conditional on $\tau$) let $X = (X_t : t\geq0, X_0=0)$, be a continuous-time simple symmetric random walk on ${\Bbb Z}$ with…
The time distribution of relaxation events in an aging system is investigated via molecular dynamics simulations. The focus is on the distribution functions of the first passage time, $p_1(\Delta t)$, and the persistence time, $p(\tau)$. In…
Many stochastic time series can be modelled by discrete random walks in which a step of random sign but constant length $\delta x$ is performed after each time interval $\delta t$. In correlated discrete time random walks (CDTRWs), the…
A dynamical model of small-world network, with directed links which describe various correlations in social and natural phenomena, is presented. Random responses of every site to the imput message are introduced to simulate real systems.…
Consider a string of $n$ positions, i.e. a discrete string of length $n$. Units of length $k$ are placed at random on this string in such a way that they do not overlap, and as often as possible, i.e. until all spacings between neighboring…
The dynamic scaling of curved interfaces presents features that are strikingly different from those of the planar ones. Spherical surfaces above one dimension are flat because the noise is irrelevant in such cases. Kinetic roughening is…
We investigate the validity of the "Einstein relations" in the general setting of unimodular random networks. These are equalities relating scaling exponents: $d_w = d_f + \tilde{\zeta}$ and $d_s = 2 d_f/d_w$, where $d_w$ is the walk…
We consider the distribution of the duration time, the time elapsed since it began, of a diffusion process given its present position, under the assumption that the process began at the origin. For unbiased diffusion, the distribution does…
We propose a simple discrete model to study the nonequilibrium fluctuations of two locally coupled 1+1 dimensional systems (interfaces). Measuring numerically the tilt-dependent velocity we construct a set of stochastic continuum equations…
We formulate a scaling theory for the long-time diffusive motion in a space occluded by a high density of moving obstacles in dimensions 1, 2 and 3. Our tracers diffuse anomalously over many decades in time, before reaching a diffusive…