Related papers: Aging Continuous Time Random Walks
We study the Tree Builder Random Walk: a randomly growing tree, built by a walker as she is walking around the tree. Namely, at each time $n$, she adds a leaf to her current vertex with probability $p_n \asymp n^{-\gamma}$, $\gamma\in…
In this article, we generalize the recent Discrete Time Random Walk (DTRW) algorithm, which was introduced for the computation of probability densities of fractional diffusion. Although it has the same computational complexity and shares…
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 analyze the effect of time dependent external field on non-Markovian migration described by the continuous time random walk (CTRW) approach. The rigorous method of treating the problem is proposed which is based on the Markovian…
The phenomenon of spatial clustering induced by death and reproduction in a population of anomalously diffusing individuals is studied analytically. The possibility of social behaviors affecting the migration strategies has been taken into…
Aging is a ubiquitous relaxation dynamic in disordered materials. It ensues after a rapid quench from an equilibrium "fluid" state into a non-equilibrium, history-dependent jammed state. We propose a physically motivated description that…
We present a graph random walk (GRW) method for the study of charge transport properties of complex molecular materials in the time-of-flight regime. The molecules forming the material are represented by the vertices of a directed weighted…
It is well known that the weak limit of a suitably scaled continuous-time random walk (CTRW) is the Brownian motion. We investigate the convergence of certain patterned random matrices whose entries are independent CTRWs and their…
A physical-mathematical approach to anomalous diffusion may be based on fractional diffusion equations and related random walk models. The fundamental solutions of these equations can be interpreted as probability densities evolving in time…
Linear theory of stationary response in thermal systems subjected to external perturbations requires to find equilibrium correlation function of the responding system variable in the absence of external perturbations. Studies of the…
We consider a class of discrete-time random walks with directed unit steps on the integer line. The direction of the steps is reversed at the time instants of events in a discrete-time renewal process and is maintained at uneventful time…
Network growth models that embody principles such as preferential attachment and local attachment rules have received much attention over the last decade. Among various approaches, random walks have been leveraged to capture such…
We introduce a heterogeneous continuous time random walk (HCTRW) model as a versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as porous or disordered media, multiscale or crowded…
Continuous-time random walks are generalisations of random walks frequently used to account for the consistent observations that many molecules in living cells undergo anomalous diffusion, i.e. subdiffusion. Here, we describe the…
We consider a recent model of random walk that recursively grows the network on which it evolves, namely the Tree Builder Random Walk (TBRW). We introduce a bias $\rho \in (0,\infty)$ towards the root, and exhibit a phase transition for…
It is proved that the distributions of scaling limits of Continuous Time Random Walks (CTRWs) solve integro-differential equations akin to Fokker-Planck Equations for diffusion processes. In contrast to previous such results, it is not…
The Continuous-Time Random Walk (CTRW) formalism can be adapted to encompass stochastic processes with memory. In this article we will show how the random combination of two different unbiased CTRWs can give raise to a process with clear…
Continuous-time random walks (CTRWs) with drift and position-dependent jumps provide a general framework for describing a wide range of natural and engineered systems. We analyze the stochastic differential equation associated with this…
It has been observed in numerous experiments, simulations, and various theoretical treatments that the spreading of particles can be modeled by the continuous-time random walk. We consider two well-known cases, i.e., Gaussian displacements…
The continuous time random walk model plays an important role in modeling of so called anomalous diffusion behaviour. One of the specific property of such model are constant time periods visible in trajectory. In the continuous time random…