Related papers: Holey Random Walks: Optics of Heterogeneous Turbid…
The random walk with hyperbolic probabilities that we are introducing is an example of stochastic diffusion in a one-dimensional heterogeneous media. Although driven by site-dependent one-step transition probabilities, the process retains…
Random-walk Monte Carlo simulations are widely used to predict the optical properties of complex, disordered materials. In presence of large heterogeneities (e.g., spatially-extended nonscattering regions in a turbid environment), an…
We study memory based random walk models to understand diffusive motion in crowded heterogeneous environment. The models considered are non-Markovian as the current move of the random walk models is determined by randomly selecting a move…
The random walk process in a nonhomogeneous medium, characterised by a L\'evy stable distribution of jump length, is discussed. The width depends on a position: either before the jump or after that. In the latter case, the density slope is…
We study a random walk in random environment on the non-negative integers. The random environment is not homogeneous in law, but is a mixture of two kinds of site, one in asymptotically vanishing proportion. The two kinds of site are (i)…
Random walks serve as important tools for studying complex network structures, yet their dynamics in cases where transition probabilities are not static remain under explored and poorly understood. Here we study nonlinear random walks that…
We consider a class of inhomogeneous media known as composite media that is often encountered in experimental sciences and investigate the persistence probability of a random walker in such a system. Analytical and numerical results for the…
We consider continuous-time random walk models described by arbitrary sojourn time probability density functions. We find a general expression for the distribution of time-averaged observables for such systems, generalizing some recent…
We develop a time domain random walk approach for conservative solute transport in heterogeneous media where medium properties vary over a distribution of length scales. The spatial transition lengths are equal to the heterogeneity length…
We study the asymptotic distribution of random walks on $\mathbb Z^d$ ($d\ge1$) in deterministic reversible environments defined by an assignment of a positive conductance to each edge of $\mathbb Z^d$. We identify a deterministic set of…
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…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
Random walks are studied on disordered cellular networks in 2-and 3-dimensional spaces with arbitrary curvature. The coefficients of the evolution equation are calculated in term of the structural properties of the cellular system. The…
We present a theoretical and experimental study of light transport in disordered media with strongly heterogeneous distribution of scatterers formed via non-scattering regions. Step correlations induced by quenched disorder are found to…
We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…
Recent progress on the understanding of the Random Conductance Model is reviewed. A particular emphasis is on homogenization results such as functional central limit theorems, local limit theorems and heat kernel estimates for almost every…
Random walks as well as diffusions in random media are considered. Methods are developed that allow one to establish large deviation results for both the `quenched' and the `averaged' case.
Dynamical systems having many coexisting attractors present interesting properties from both fundamental theoretical and modelling points of view. When such dynamics is under bounded random perturbations, the basins of attraction are no…
A particle subject to successive, random displacements is said to execute a random walk (in position or some other coordinate). The mathematical properties of random walks have been very thoroughly investigated, and the model is used in…
We consider a random walk model in a one-dimensional environment, formed by several zones of finite width with the fixed transition probabilities. It is also assumed that the transitions to the left and right neighboring points have unequal…