Related papers: Infinite densities for L\'evy walks

Diffusion is the macroscopic manifestation of disordered molecular motion. Mathematically, diffusion equations are partial differential equations describing the fluid-like large-scale dynamics of parcels of molecules. Spatially…

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 consider a multidimensional random walk in a product random environment with bounded steps, transience in some spatial direction, and high enough moments on the regeneration time. We prove an invariance principle, or functional central…

Stochastic processes are shown to emerge from the time evolution of complex quantum systems. Using parametric, banded random matrix ensembles to describe a quantum chaotic environment, we show that the dynamical evolution of a particle…

Properties of random and fluctuating systems are often studied through the use of Gaussian distributions. However, in a number of situations, rare events have drastic consequences, which can not be explained by Gaussian statistics.…

We study an infinite system of moving particles, where each particle is of type A or B. Particles perform independent random walks at rates D_A>0 and D_B>0, and the interaction is given by mutual annihilation A+B->0. The initial condition…

We study occupation time statistics in ergodic continuous-time random walks. Under thermal detailed balance conditions, the average occupation time is given by the Boltzmann-Gibbs canonical law. But close to the non-ergodic phase, the…

The unified description of diffusion processes that cross over from a ballistic behavior at short times to normal or anomalous diffusion (sub- or superdiffusion) at longer times is constructed on the basis of a non-Markovian generalization…

A criterion for proving a strong form of propagation of chaos on the path space, known as entropy chaos, for a general interacting diffusion system is proposed. Our analysis focuses on the class of conservative diffusions introduced by…

We consider a model system of persistent random walkers that can jam, pass through each other or jump apart (recoil) on contact. In a continuum limit, where particle motion between stochastic changes in direction becomes deterministic, we…

A simple model for the nonlinear collective transport of interacting particles in a random medium with strong disorder is introduced and analyzed. A finite threshold for the driving force divides the behavior into two regimes characterized…

A one-dimensional system of nonintersecting Brownian particles is constructed as the diffusion scaling limit of Fisher's vicious random walk model. $N$ Brownian particles start from the origin at time $t=0$ and undergo mutually avoiding…

The kinetics of the annihilation process, $A+A\to 0$, with ballistic particle motion is investigated when the distribution of particle velocities is {\it discrete}. This discreteness is the source of many intriguing phenomena. In the mean…

The diffusion of a particle in a crowded environment typically proceeds through three regimes: for very short times the particle diffuses freely until it collides with an obstacle for the first time, while for very long times diffusion the…

We have studied a model of a random walk in a quenched random environment. In addition to featuring anomalous diffusion and localization, for special regimes of disorder parameters the particle density decomposes into multi-Gaussian…

This paper concerns the propagation of particles through a quenched random medium. In the one- and two-dimensional models considered, the local dynamics is given by expanding circle maps and hyperbolic toral automorphisms, respectively. The…

We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight…

We investigate the dynamic impact of heterogeneous environments on superdiffusive random walks known as L\'evy flights. We devote particular attention to the relative weight of source and target locations on the rates for spatial…

In classical diffusion, particle step-sizes have a Gaussian distribution. However, in superdiffusion, they have power-law tails, with transport dominated by rare, long L\'evy flights. Similarly, if the time interval between scattering…

We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a…