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We study the motion of a particle sliding under the action of an external field on a stochastically fluctuating one-dimensional Edwards-Wilkinson surface. Numerical simulations using the single-step model shows that the mean-square…

Statistical Mechanics · Physics 2009-11-10 Manoj Gopalakrishnan

We study the random growth of surfaces from within the perspective of a single column, namely, the fluctuation of the column height around the mean value, y(t)= h(t)-< h(t)>, which is depicted as being subordinated to a standard…

Adaptation and Self-Organizing Systems · Physics 2009-11-10 R. Failla , P. Grigolini , M. Ignaccolo , A. Schwettmann

We consider a system of multiscale stochastic differential equations whose slow component is drivenby a fractional Brownian motion with Hurst parameter H greater than 1/2. Under ergodic assumptions ensuring the applicability of the…

Probability · Mathematics 2025-12-10 Xue-Mei Li , Colin Piernot , Szymon Sobczak , Kexing Ying

We consider a system of diffusing particles on the real line in a quadratic external potential and with repulsive electrostatic interaction. The empirical measure process is known to converge weakly to a deterministic measure-valued process…

Probability · Mathematics 2010-03-23 Martin Bender

We investigate fluctuation phenomena for the graph distance and the number of cut points associated with random media arising from the range of a random walk. Our results demonstrate a sequence of dimension-dependent phase transitions in…

Probability · Mathematics 2026-03-18 Arka Adhikari , Izumi Okada

The scaling properties of the roughness of surfaces grown by two different processes randomly alternating in time, are addressed. The duration of each application of the two primary processes is assumed to be independently drawn from given…

Statistical Mechanics · Physics 2009-11-07 Subhadip Raychaudhuri , Yonathan Shapir

In a system made up of independent random walks, fluctuations of order $n^{1/4}$ from the hydrodynamic limit come from particle current across characteristics. We show that a two-parameter space-time particle current process converges to a…

Probability · Mathematics 2008-10-29 Rohini Kumar

Inhomogeneities in deposition may lead to formation of rough surfaces, whose height fluctuations can be probed directly by scanning microscopy, or indirectly by scattering. Analytical or numerical treatments of simple growth models suggest…

Condensed Matter · Physics 2009-10-28 Mehran Kardar

Consider a system of particles evolving as independent and identically distributed (i.i.d.) random walks. Initial fluctuations in the particle density get translated over time with velocity $\vec{v}$, the common mean velocity of the random…

Probability · Mathematics 2010-09-15 Rohini Kumar

We study the average shape of a fluctuation of a time series x(t), that is the average value <x(t)-x(0)>_T before x(t) first returns, at time T, to its initial value x(0). For large classes of stochastic processes we find that a scaling law…

Statistical Mechanics · Physics 2009-11-10 Andrea Baldassarri , Francesca Colaiori , Claudio Castellano

We study the equilibrium fluctuations for a gradient exclusion process with conductances in random environments, which can be viewed as a central limit theorem for the empirical distribution of particles when the system starts from an…

Probability · Mathematics 2011-04-08 Jonathan Farfan , Alexandre B. Simas , Fabio J. Valentim

The temporal evolution of equilibrium fluctuations for surface steps of monoatomic height is analyzed studying one-dimensional solid-on-solid models. Using Monte Carlo simulations, fluctuations due to periphery-diffusion (PD) as well as due…

Statistical Mechanics · Physics 2014-07-31 Walter Selke

In this paper, we analyze the random fluctuations in a one dimensional stochastic homogenization problem and prove a central limit result, i.e., the first order fluctuations can be described by a Gaussian process that solves an SPDE with…

Probability · Mathematics 2015-08-24 Yu Gu

We study an anomalous behavior of the height fluctuation width in the crossover from random to coherent growths of surface for a stochastic model. In the model, random numbers are assigned on perimeter sites of surface, representing pinning…

Statistical Mechanics · Physics 2009-10-28 K. Park , B. Kahng

We consider the multi-point equal time height fluctuations of a one-dimensional polynuclear growth model in a half space. For special values of the nucleation rate at the origin, the multi-layer version of the model is reduced to a…

Statistical Mechanics · Physics 2007-05-23 T. Sasamoto , T. Imamura

We demonstrate the non-universal behavior of finite size scaling in (1+1) dimension of a nonlinear discrete growth model involving extended particles in generalized point of view. In particular, we show the violation of the universal nature…

Statistical Mechanics · Physics 2009-11-25 Pradipta Kumar Mandal , Debnarayan Jana

We consider the multi-time correlation and covariance structure of a random surface growth with a wall introduced in arXiv:0904.2607. It is shown that the correlation functions associated with the model along space-like paths have…

Probability · Mathematics 2022-03-31 Zhengye Zhou

We consider a system of $N$ disordered mean-field interacting diffusions within spatial constraints: each particle $\theta_i$ is attached to one site $x_i$ of a periodic lattice and the interaction between particles $\theta_i$ and…

Probability · Mathematics 2020-01-16 Eric Luçon , Wilhelm Stannat

In this work we introduce correlated random walks on $\Z$. When picking suitably at random the coefficient of correlation, and taking the average over a large number of walks, we obtain a discrete Gaussian process, whose scaling limit is…

Probability · Mathematics 2007-05-23 Enriquez Nathanael

Fluctuation scaling is observed phenomenon from complex networks through finance to ecology. It means that the variance and the mean of a specific quantity are related as $\ev{\sigma^2|n}\propto \ev{n|A}^{2\alpha}$ with $1/2\geq \alpha \geq…

Physics and Society · Physics 2008-12-02 Zoltan Eisler , Janos Kertesz