Related papers: Continuous Time Random Walks with Internal Dynamic…
The modeling and simulation of stochastic reaction-diffusion processes is a topic of steady interest that is approached with a wide range of methods. \rev{At the level of particle-resolved descriptions, where chemical reactions are coupled…
We analyze two models of subdiffusion with stochastic resetting. Each of them consists of two parts: subdiffusion based on the continuous-time random walk (CTRW) scheme and independent resetting events generated uniformly in time according…
We apply the formalism of the continuous time random walk to the study of financial data. The entire distribution of prices can be obtained once two auxiliary densities are known. These are the probability densities for the pausing time…
In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm was already introduced in both the Brownian context and in the Ornstein-Uhlenbeck context. Here…
Continuous time random walks impose a random waiting time before each particle jump. Scaling limits of heavy tailed continuous time random walks are governed by fractional evolution equations. Space-fractional derivatives describe heavy…
Quantum random walks are shown to have non-intuitive dynamics which makes them an attractive area of study for devising quantum algorithms for long-standing open problems as well as those arising in the field of quantum computing. In the…
The various types of generalized Cattaneo, called also telegrapher's equation, are studied. We find conditions under which solutions of the equations considered so far can be recognized as probability distributions, \textit{i.e.} are…
Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs,…
Transport phenomena play a crucial role in modern physics and applied sciences. Examples include the dissipation of energy across a large system, the distribution of quantum information in optical networks, and the timely modeling of…
Discrete-time quantum walks (DTQWs) in random artificial electric and gravitational fields are studied analytically and numerically. The analytical computations are carried by a new method which allows a direct exact analytical…
Invasion phenomena for heterogeneous reaction-diffusion equations are contemporary and challenging questions in applied mathematics. In this paper we are interested in the question of spreading for a reaction-diffusion equation when the…
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…
The theory of diffusion seeks to describe the motion of particles in a chaotic environment. Classical theory models individual particles as independent random walkers, effectively forgetting that particles evolve together in the same…
Experimental studies of the diffusion of biomolecules in the environment of biological cells are routinely confronted with multiple sources of stochasticity, whose identification renders the detailed data analysis of single molecule…
In this paper, we derive explicit formulas for the surface averaged first exit time of a discrete random walk on a finite lattice. We consider a wide class of random walks and lattices, including random walks in a non-trivial potential…
Motivated by studies on the recurrent properties of animal and human mobility, we introduce a path-dependent random walk model with long range memory for which not only the mean square displacement (MSD) can be obtained exactly in the…
We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the…
We investigate three different methods for systematically approximating the diffusion coefficient of a deterministic random walk on the line which contains dynamical correlations that change irregularly under parameter variation. Capturing…
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…
We consider a new model of quantum walk on a one-dimensional momentum space that includes both discrete jumps and continuous drift. Its time evolution has two stages; a Markov diffusion followed by localized dynamics. As in the well known…