Related papers: Diffusivity in one-dimensional generalized Mott va…
Thermal diffusion has been studied for over 150 years. Despite of the long history and the increasing importance of the phenomenon, the physics of thermal diffusion remains poorly understood. In this paper Ludwig's thermal diffusion is…
We investigate, both analytically and with numerical simulations, a Monte Carlo dynamics at zero temperature, where a random walker evolving in continuous space and discrete time seeks to minimize its potential energy, by decreasing this…
Diffusion in a multidimensional energy surface with minima and barriers is a problem of importance in statistical mechanics and also has wide applications, such as protein folding. To understand it in such a system, we carry out theory and…
We study arithmetic properties of short uniform random walks in arbitrary dimensions, with a focus on explicit (hypergeometric) evaluations of the moment functions and probability densities in the case of up to five steps. Somewhat to our…
We study, on a $d$ dimensional hypercubic lattice, a random walk which is homogeneous except for one site. Instead of visiting this site, the walker hops over it with arbitrary rates. The probability distribution of this walk and the…
Mott's variable range hopping (v.r.h.) is the phonon-induced hopping of electrons in disordered solids (such as doped semiconductors) within the regime of strong Anderson localization. It was introduced by N.~Mott to explain the anomalous…
The diffusion equation and its time-fractional counterpart can be obtained via the diffusion limit of continuous-time random walks with exponential and heavy-tailed waiting time distributions. The space dependent variable-order…
We prove that random walks in random environments, that are exponentially mixing in space and time, are almost surely diffusive, in the sense that their scaling limit is given by the Wiener measure.
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 derive a perturbation expansion for general self-interacting random walks, where steps are made on the basis of the history of the path. Examples of models where this expansion applies are reinforced random walk, excited random walk, the…
We consider a model of random walk in ${\mathbb Z}^2$ with (fixed or random) orientation of the horizontal lines (layers) and with non constant iid probability to stay on these lines. We prove the transience of the walk for any fixed…
We study the dynamics of a generalization of quantum coin walk on the line which is a natural model for a diffusion modified by quantum or interference effects. In particular, our results provide surprisingly simple explanations to…
We present a model for variations in atmospheric temperature from time scales of one day to one million years based on a stochastic diffusion (random walk) model of the turbulent transport of heat energy vertically in a coupled…
Superslow diffusion, i.e., the long-time diffusion of particles whose mean-square displacement (variance) grows slower than any power of time, is studied in the framework of the decoupled continuous-time random walk model. We show that this…
The diffusion of a walk in the presence of traps is investigated. Different diffusion regimes are obtained considering the magnitude of the fluctuations in waiting times and jump distances. A constant velocity during the jump motion is…
Traditionally, time-development of the mean square displacement has been employed to determine the diffusion coefficient from the trajectories of single particles. However, this approach is sensitive to the noise and the motion blur upon…
We develop a mesoscopic modeling framework for diffusion in a crowded environment, particularly targeting applications in the modeling of living cells. Through homogenization techniques we effectively coarse-grain a detailed microscopic…
We consider a random walk on the support of an ergodic simple point process on R^d, d>1, furnished with independent energy marks. The jump rates of the random walk decay exponentially in the jump length and depend on the energy marks via a…
A fundamental insight in the theory of diffusive random walks is that the mean length of trajectories traversing a finite open system is independent of the details of the diffusion process. Instead, the mean trajectory length depends only…
A correlated Gaussian random walk(CGRW) model is proposed as a simple model of animal dispersal. The general features of CGRW is described. We will discuss how from this single model a number of different kinds of correlated random walk can…