Related papers: Scaling limits of L\'evy walks with random velocit…
We consider transport properties for a non-homogeneous persistent random walk, that may be viewed as a mean-field version of the L\'evy-Lorentz gas, namely a 1-d model characterized by a fat polynomial tail of the distribution of…
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…
Recent research highlighted the scaling property of human and animal mobility. An interesting issue is that the exponents of scaling law for animals and humans in different situations are quite different. This paper proposes a general…
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 compute the average shape of trajectories of some one--dimensional stochastic processes x(t) in the (t,x) plane during an excursion, i.e. between two successive returns to a reference value, finding that it obeys a scaling form. For…
This paper considers the optimal scaling problem for high-dimensional random walk Metropolis algorithms for densities which are differentiable in Lp mean but which may be irregular at some points (like the Laplace density for example)…
We study a queueing network with a strictly upper-triangular routing matrix, where each column contains at most one non-negative entry, and the root node receives input from a spectrally positive L\'{e}vy process. Our aim is to characterize…
We obtain sample-path large deviations for a class of one-dimensional stochastic differential equations with bounded drifts and heavy-tailed L\'evy processes. These heavy-tailed L\'evy processes do not satisfy the exponential integrability…
We consider the distribution of the duration time, the time elapsed since it began, of a diffusion process given its present position, under the assumption that the process began at the origin. For unbiased diffusion, the distribution does…
We study the causes of anomalous dispersion in Darcy-scale porous media characterized by spatially heterogeneous hydraulic properties. Spatial variability in hydraulic conductivity leads to spatial variability in the flow properties through…
We investigate the impact of external periodic potentials on superdiffusive random walks known as Levy flights and show that even strongly superdiffusive transport is substantially affected by the external field. Unlike ordinary random…
In a continuous time random walk (CTRW), each random jump follows a random waiting time. CTRW scaling limits are time-changed processes that model anomalous diffusion. The outer process describes particle jumps, and the non-Markovian inner…
The evolution of infinitesimal, localized perturbations is investigated in a one-dimensional diatomic gas of hard-point particles (HPG) and thereby connected to energy diffusion. As a result, a Levy walk description, which was so far…
Charge transport processes in disordered complex media are accompanied by anomalously slow relaxation for which usually a broad distribution of relaxation times is adopted. To account for those properties of the environment, a standard…
Recent experiments (G. Ariel, et al., Nature Comm. 6, 8396 (2015)) revealed an intriguing behavior of swarming bacteria: they fundamentally change their collective motion from simple diffusion into a superdiffusive L\'{e}vy walk dynamics.…
In this paper we first provide several conditional limit theorems for L\'evy processes with negative drift and regularly varying tail. Then we apply them to study the asymptotic behavior of expectations of some exponential functionals of…
L\'evy Flights are paradigmatic generalised random walk processes, in which the independent stationary increments---the "jump lengths"---are drawn from an $\alpha$-stable jump length distribution with long-tailed, power-law asymptote. As a…
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…
The uniform spanning tree (UST) and the loop-erased random walk (LERW) are related probabilistic processes. We consider the limits of these models on a fine grid in the plane, as the mesh goes to zero. Although the existence of scaling…
Anomalous scaling in the statistics of an active scalar in homogeneous turbulent convection is studied using a dynamical shell model. We extend refined similarity ideas for homogeneous and isotropic turbulence to homogeneous turbulent…