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The usual development of the continuous time random walk (CTRW) assumes that jumps and time intervals are a two-dimensional set of independent and identically distributed random variables. In this paper we address the theoretical setting of…

Data Analysis, Statistics and Probability · Physics 2008-09-29 Miquel Montero , Jaume Masoliver

A continuous time random walk (CTRW) is a random walk in which both spatial changes represented by jumps and waiting times between the jumps are random. The CTRW is coupled if a jump and its preceding or following waiting time are dependent…

Probability · Mathematics 2016-03-14 Adam Barczyk , Peter Kern

Systems living in complex non equilibrated environments often exhibit subdiffusion characterized by a sublinear power-law scaling of the mean square displacement. One of the most common models to describe such subdiffusive dynamics is the…

Statistical Mechanics · Physics 2015-07-03 Andrea Cairoli , Adrian Baule

We consider the dynamics of a separable Continuous Time Random Walk (CTRW) when the random walker is biased by a velocity field in a uniformly growing domain. Concrete examples for such domains include growing biological cells or lipid…

Statistical Mechanics · Physics 2020-08-26 F. Le Vot , E. Abad , R. Metzler , S. B. Yuste

We investigate the dynamics of a particle executing a general Continuous Time Random Walk (CTRW) in three dimensions under the influence of arbitrary time-varying external fields. Contrary to the general approach in recent works, our method…

Statistical Mechanics · Physics 2011-12-15 Shovan Dutta , Subhankar Ray , J. Shamanna

Levy flights and fractional Brownian motion (fBm) have become exemplars of the heavy tailed jumps and long-ranged memory widely seen in physics. Natural time series frequently combine both effects, and linear fractional stable motion (lfsm)…

Mathematical Physics · Physics 2011-08-25 N. W. Watkins , D. Credgington , R. Sanchez , S. J. Rosenberg , S. C. Chapman

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, $P_t$,…

Statistical Mechanics · Physics 2017-01-19 Shahar Amitai , Raphael Blumenfeld

The standard diffusion processes are known to be obtained as the limits of appropriate random walks. These prelimiting random walks can be quite different however. The diffusion coefficient can be made responsible for the size of jumps or…

Probability · Mathematics 2022-03-10 Vassili N. Kolokoltsov

A novel version of the Continuous-Time Random Walk (CTRW) model with memory is developed. This memory means the dependence between arbitrary number of successive jumps of the process, while waiting times between jumps are considered as…

Data Analysis, Statistics and Probability · Physics 2016-12-16 Tomasz Gubiec , Ryszard Kutner

Continuous Time Random Walk models (CTRW) of anomalous diffusion are studied, where the anomalous exponent $\beta(x) \in (0,1)$ varies in space. This type of situation occurs e.g. in biophysics, where the density of the intracellular matrix…

Statistical Mechanics · Physics 2018-03-13 Peter Straka

We demonstrate that continuous time random walks in which successive waiting times are correlated by Gaussian statistics lead to anomalous diffusion with mean squared displacement <r^2(t)>~t^{2/3}. Long-ranged correlations of the waiting…

Statistical Mechanics · Physics 2015-05-14 Vincent Tejedor , Ralf Metzler

The continuous time random walk (CTRW) approach has been widely applied to model large-scale non-Fickian transport in the flow through disordered media. Often, the underlying microscopic transport mechanisms and disorder characteristics are…

Fluid Dynamics · Physics 2024-03-12 Xiangnan Yu , Marco Dentz , HongGuang Sun , Yong Zhang

Levy flights and fractional Brownian motion (fBm) have become exemplars of the heavy tailed jumps and long-ranged memory seen in space physics and elsewhere. Natural time series frequently combine both effects, and Linear Fractional Stable…

Mathematical Physics · Physics 2008-03-20 Nicholas W. Watkins , Daniel Credgington , Raul Sanchez , Sandra C. Chapman

We study continuous time random walks (CTRW) with power law distribution of waiting times under resetting which brings the walker back to the origin, with a power-law distribution of times between the resetting events. Two situations are…

Statistical Mechanics · Physics 2020-07-01 Anna S. Bodrova , Igor M. Sokolov

We show that, in a broad class of continuous time random walks (CTRW), a small external field can turn diffusion from standard into anomalous. We illustrate our findings in a CTRW with trapping, a prototype of subdiffusion in disordered and…

Disordered Systems and Neural Networks · Physics 2015-06-12 R. Burioni , G. Gradenigo , A. Sarracino , A. Vezzani , A. Vulpiani

We show the asymptotic long-time equivalence of a generic power law waiting time distribution to the Mittag-Leffler waiting time distribution, characteristic for a time fractional CTRW. This asymptotic equivalence is effected by a…

Statistical Mechanics · Physics 2008-05-18 Rudolf Gorenflo , Francesco Mainardi

Continuous Time Random Walks (CTRW) are widely used to coarse-grain the evolution of systems jumping from a metastable sub-set of their configuration space, or trap, to another via rare intermittent events. The multi-scaled behavior typical…

Statistical Mechanics · Physics 2014-01-21 Paolo Sibani

In this paper we study controlled continuous time random walks (CTRWs) and heuristically derive pay-off function dynamic programming (DP) equations which turn in the limit of standard scaling to fractional Hamilton Jacobi Bellman type…

Optimization and Control · Mathematics 2012-04-05 V. Kolokoltsov , M. Veretennikova

Continuous-time random walk (CTRW) is a model of anomalous sub-diffusion in which particles are immobilized for random times between successive jumps. A power-law distribution of the waiting times, $\psi(\tau) \tau^{-(1+\alpha)}$, leads to…

Statistical Mechanics · Physics 2011-12-06 Shai Carmi , Eli Barkai

We consider the continuous time random walk model (CTRW) of tracer's motion in porous medium flows based on the experimentally determined distributions of pore velocity and pore size reported in Holzner et al. Phys. Rev. E 92, 013015…

Statistical Mechanics · Physics 2017-05-31 Itzhak Fouxon , Markus Holzner