Related papers: L\'evy walk dynamics in an external harmonic poten…
The Weierstrass random walk is a paradigmatic Markov chain giving rise to a L\'evy-type superdiffusive behavior. It is well known that Special Relativity prevents the arbitrarily high velocities necessary to establish a superdiffusive…
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…
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…
Time-averaged autocorrelation functions of a dichotomous random process switching between 1 and 0 and governed by wide power law sojourn time distribution are studied. Such a process, called a L\'evy walk, describes dynamical behaviors of…
The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…
We consider stochastic systems involving general -- non-Gaussian and asymmetric -- stable processes. The random quantities, either a stochastic force or a waiting time in a random walk process, explicitly depend on the position. A…
The paper is devoted to the relationship between the continuous Markovian description of Levy flights developed previously and their equivalent representation in terms of discrete steps of a wandering particle, a certain generalization of…
The Levy walk model is studied in the context of the anomalous heat conduction of one dimensional systems. In this model the heat carriers execute Levy-walks instead of normal diffusion as expected in systems where Fourier's law holds. Here…
The L\'evy walk model is a stochastic framework of enhanced diffusion with many applications in physics and biology. Here we investigate the time averaged mean squared displacement $\bar{\delta^2}$ often used to analyze single particle…
We study sums of independent and identically distributed random velocities in special relativity. We show that the resulting one-dimensional velocity distributions are not only stable under relativistic velocity addition but define a…
In search for mathematically tractable models of anomalous diffusion, we introduce a simple dynamical system consisting of a chain of coupled maps of the interval whose Lyapunov exponents vanish everywhere. The volume preserving property…
L\'evy noise influences diverse non-equilibrium systems across scales, including quantum devices, active biological matter, and financial markets. While such noise is pervasive, its overall impact on activated transitions between metastable…
Levy walk at the finite velocity is considered. To analyze the spatial and temporal characteristics of this process, the method of moments has been used. The asymptotic distributions of the moments (at $t\to\infty$) have been obtained for…
A random walk $w_n$ on a separable, geodesic hyperbolic metric space $X$ converges to the boundary $\partial X$ with probability one when the step distribution supports two independent loxodromics. In particular, the random walk makes…
Random walks provide a simple conventional model to describe various transport processes, for example propagation of heat or diffusion of matter through a medium. However, in many practical cases the medium is highly irregular due to…
We study the distribution of occupation times for a one-dimensional random walk restricted to a finite interval by reflecting boundary conditions. At short times the classical bimodal distribution due to L\'evy is reproduced with walkers…
Memory effects, sometimes, can not be neglected. In the framework of continuous time random walk, memory effect is modeled by the correlated waiting times. In this paper, we derive the two-point probability distribution of the stochastic…
We propose a variety of models of random walk, discrete in space and time, suitable for simulating stable random variables of arbitrary index $\alpha$ ($0< \alpha \le 2$), in the symmetric case. We show that by properly scaled transition to…
Levy flights and subdiffusive processes and their properties are discussed. We derive the space- and time-fractional transport equations, and consider their solutions in external potentials. An extensive list of references is included.
We consider correlated L\'evy walks on a class of two- and three-dimensional deterministic self-similar structures, with correlation between steps induced by the geometrical distribution of regions, featuring different diffusion properties.…