Related papers: L\'evy flights with power-law absorption
We consider a discrete time simple symmetric random walk on Z^d, d>=1, where the path of the walk is perturbed by inserting deterministic jumps. We show that for any time n and any deterministic jumps that we insert, the expected number of…
We investigate multiple scattering of near-resonant light in a Doppler-broadened atomic vapor. We experimentally characterize the length distribution of the steps between successive scattering events. The obtained power law is…
The propagation of light that undergoes multiple-scattering by resonant atomic vapor can be described as a L\'evy flight. L\'evy flight is a random walk with heavy tailed step-size (r) distribution, decaying asymptotically as $P(r)\sim…
The dynamics of the survival probability of quantum walkers on a one-dimensional lattice with random distribution of absorbing immobile traps are investigated. The survival probability of quantum walkers is compared with that of classical…
Exploration and trapping properties of random walkers that may evanesce at any time as they walk have seen very little treatment in the literature, and yet a finite lifetime is a frequent occurrence, and its effects on a number of random…
We present theoretical and experimental results of L\'evy flights of light originating from a random walk of photons in a hot atomic vapor. In contrast to systems with quenched disorder, this system does not present any correlations between…
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.…
In this paper we consider the one-dimensional, biased, randomly trapped random walk when the trapping times have infinite variance. We prove sufficient conditions for the suitably scaled walk to converge to a transformation of a stable…
We present a stochastic lattice theory describing the kinetic behavior of trapping reactions $A + B \to B$, in which both the $A$ and $B$ particles perform an independent stochastic motion on a regular hypercubic lattice. Upon an encounter…
Continuous time random walks and Langevin equations are two classes of stochastic models for describing the dynamics of particles in the natural world. While some of the processes can be conveniently characterized by both of them, more…
We have investigated the random walk problem in a finite system and studied the crossover induced in the the persistence probability scales by the system size.Analytical and numerical work show that the scaling function is an exponentially…
We consider a continuous time random walk $X$ in random environment on $\Z^+$ such that its potential can be approximated by the function $V: \R^+\to \R$ given by $V(x)=\sig W(x) -\frac{b}{1-\alf}x^{1-\alf}$ where $\sig W$ a Brownian motion…
We consider a new model of a branching random walk on a multidimensional lattice with continuous time and one source of particle reproduction and death, as well as an infinite number of sources in which, in addition to the walk, only…
The L\'evy walk is a non-Brownian random walk model that has been found to describe anomalous dynamic phenomena in diverse fields ranging from biology over quantum physics to ecology. Recurrently occurring problems are to examine whether…
We study the problem of random search in finite networks with a tree topology, where it is expected that the distribution of the first-passage time F(t) decays exponentially. We show that the slope of the exponential tail is independent of…
We consider the motion of an overdamped particle in a periodic potential lacking spatial symmetry under the influence of symmetric L\'evy noise, being a minimal setup for a ``L\'evy ratchet.'' Due to the non-thermal character of the L\'evy…
We study finite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which…
Building upon the knowledge of the distribution of the first positive position reached by a random walker starting from the origin, one can derive new results on the statistics of the gap between the largest and second-largest positions of…
We have studied a random walk model based on majority rule. At a given instant, the moving direction of a cargo is determined by motor coordination mediated by a tug-of-war mechanism between two kinds of competing motor proteins. We have…
We study the work fluctuations of a particle subjected to a deterministic drag force plus a random forcing whose statistics is of the L\'evy type. In the stationary regime, the probability density of the work is found to have ``fat''…