Related papers: From continuous-time random walks to controlled-di…
We introduce the concept of Randomly Modulated Gaussian Processes as a unifying framework for modeling, analyzing and classifying anomalous diffusion models in heterogeneous media. This formulation incorporates correlations in the…
The continuous-time random walk (CTRW) model is useful for alleviating the computational burden of simulating diffusion in actual media. In principle, isotropic CTRW only requires knowledge of the step-size, $P_l$, and waiting-time, $P_t$,…
We discuss here in detail a new analytical random walk approach to calculating the phase-diagram for spatially extended systems with multiplicative noise. We use the Anderson localization problem as an example. The transition from…
Continuous time random walks are non-Markovian stochastic processes, which are only partly characterized by single-time probability distributions. We derive a closed evolution equation for joint two-point probability density functions of a…
Expanding medium is very common in many different fields, such as biology and cosmology. It brings a nonnegligible influence on particle's diffusion, which is quite different from the effect of an external force field. The dynamic mechanism…
The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems…
Theory of diffusion-mediated reactions is already established for the target problem in the dilute limit, where the immobile target is surrounded by many quenchers. For lattice random walks in the crowded situation, each quencher is…
We show that anomalous diffusion can result when the steps of a random walk are not statistically independent. We present an algorithm that counts all the possible paths of particles diffusing on random graphs with arbitrary degree…
We consider a population of $N$ labeled random walkers moving on a substrate, and an excitation jumping among the walkers upon contact. The label $\mathcal{X}(t)$ of the walker carrying the excitation at time $t$ can be viewed as a…
A power-law distance-dependent biased random walk model with a tuning parameter ($\sigma$) is introduced in which finite mean first passage times are realizable if $\sigma$ is less than a critical value $\sigma_c$. We perform numerical…
The standard diffusive spreading, characterized by a Gaussian distribution with mean square displacement that grows linearly with time, can break down, for instance, under the presence of correlations and heterogeneity. In this work, we…
In this paper we study the asymptotic behavior of the Random-Walk Metropolis algorithm on probability densities with two different `scales', where most of the probability mass is distributed along certain key directions with the…
We study the asymptotic behaviour of a random walk whose evolution is dependent on the state of an itself dynamically evolving environment. In particular, we extend our previous results in [Bethuelsen and V\"ollering, 2016] and prove a…
In this work the diffusion in the quenched trap model with diverging mean waiting times is examined. The approach of randomly stopped time is extensively applied in order to obtain asymptotically exact representation of the disorder…
Encounters between walkers performing a random motion on an appropriate structure can describe a wide variety of natural phenomena ranging from pharmacokinetics to foraging. On homogeneous structures the asymptotic encounter probability…
Models of reaction diffusion processes usually employ discrete lattice models with particles interacting at the same site, resulting in localized reactions in the continuum limit. Here, various non-local interactions are considered, and two…
We analyse how simple local constraints in two dimensions lead a defect to exhibit robust, non-transient, and tunable, subdiffusion. We uncover a rich dynamical phenomenology realised in ice- and dimer-type models. On the microscopic scale…
We study a one-dimensional random walk with memory in which the step lengths to the left and to the right evolve at each step in order to reduce the wandering of the walker. The feedback is quite efficient and lead to a non-diffusive walk.…
We investigate random walks on a lattice with imperfect traps. In one dimension, we perturbatively compute the survival probability by reducing the problem to a particle diffusing on a closed ring containing just one single trap. Numerical…
Via a Dirichlet form extension theorem and making full use of two-sided heat kernel estimates, we establish quenched invariance principles for random walks in random environments with a boundary. In particular, we prove that the random walk…