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The explicit determinations of the mean first-passage time (MFPT) for trapping problem are limited to some simple structure, e.g., regular lattices and regular geometrical fractals, and determining MFPT for random walks on other media,…

For stochastic growth models in the Kardar-Parisi-Zhang (KPZ) class in 1+1 dimensions, fluctuations grow as t^{1/3} during time t and the correlation length at a fixed time scales as t^{2/3}. In this note we discuss the scale of time…

{\em NOTE: This paper presented the first attempt to tackle the Kardar-Parisi-Zhang (KPZ) equation using non-perturbative renormalisation group (NPRG) methods. It exploited the most natural and frequently used approximation scheme within…

We study the synchronization of two spatially extended dynamical systems where the models have imperfections. We show that the synchronization error across space can be visualized as a rough surface governed by the Kardar-Parisi-Zhang…

Growth in crystals can be { usually } described by field equations such as the Kardar-Parisi-Zhang (KPZ) equation. While the crystalline structure can be characterized by Euclidean geometry with its peculiar symmetries, the growth dynamics…

The flow in a Hele-Shaw cell with a time-increasing gap poses a unique shrinking interface problem. When the upper plate of the cell is lifted perpendicularly at a prescribed speed, the exterior less viscous fluid penetrates the interior…

Studies on hadron interactions from lattice QCD are reviewed. The $S$-wave $\pi\pi$ scattering lengths of the I=0 and I=2 channels are extracted from various lattice determinations of low energy constants in $N_f=2$ chiral perturbation…

The global effects of sudden changes in the interface growth dynamics are studied using models of the Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) classes during their growth regimes in dimensions $d=1$ and $d=2$. Scaling arguments…

Tracking the sign of fluctuations governed by the $(1+1)$-dimensional Kardar-Parisi-Zhang (KPZ) universality class, we show, both experimentally and numerically, that its evolution has an unexpected link to a simple stochastic model called…

The Kardar-Parisi-Zhang (KPZ) equation is a stochastic partial differential equation which is derived from various microscopic models, and to establish a robust way to derive the KPZ equation is a fundamental problem both in mathematics and…

We study numerically the geometrical and free-energy fluctuations of a static one-dimensional (1D) interface with a short-range elasticity, submitted to a quenched random-bond Gaussian disorder of finite correlation length $\xi>0$, and at…

The statistics of the iso-height lines in (2+1)-dimensional Kardar-Parisi-Zhang (KPZ) model is shown to be conformal invariant and equivalent to those of self-avoiding random walks. This leads to a rich variety of new exact analytical…

I characterize the extreme location and extreme first passage time of a system of $N$ particles independently diffusing in a space-time random environment. I show these extreme statistics are governed by the Kardar-Parisi-Zhang (KPZ)…

We consider the scaling limits for a one-dimensional random growth model, the weakly asymmetric single step Solid-on-Solid process. We show that the fluctuation field, if considered in an appropriate (long) space-time scale, solves the…

This work addresses the superdiffusive motion of a discrete time random walker on ordered discrete substrates and complex networks with the presence of long-range interactions (LRIs). In ordered regular lattices, where LRIs have a clear…

We consider the narrow wedge solution to the Kardar-Parisi-Zhang stochastic PDE under the characteristic $3:2:1$ scaling of time, space and fluctuations. We study the correlation of fluctuations at two different times. We show that when the…

Large-scale fading (LSF) between interacting nodes is a fundamental element in radio communications, responsible for weakening the propagation, and thus worsening the service quality. Given the importance of channel-losses in general, and…

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 =…

Critical wetting transitions under nonequilibrium conditions are studied numerically and analytically by means of an interface-displacement model defined by a Kardar-Parisi-Zhang equation, plus some extra terms representing a limiting,…

In this paper, we consider the Hartree equation with smooth but long-range interaction in the semi-classical regime, in three-dimensional space. We show that the density function of small-data solution decays at the optimal rate. When the…