Related papers: Cooling gases with Levy flights: using the general…
Levy walks are random processes with an underlying spatiotemporal coupling. This coupling penalizes long jumps, and therefore Levy walks give a proper stochastic description for a particle's motion with broad jump length distribution. We…
Diffusion occurs in numerous physical systems throughout nature, drawing its generality from the universality of the central limit theorem. Around a century ago it was realized that an extension to this type of dynamics can be obtained in…
First, we prove a \emph{local almost sure central limit theorem} for lattice random walks in the plane. The corresponding version for random walks in the line was considered by the author in \cite{5}. This gives us a quantitative version of…
We consider the A + A --> emptyset reaction, where the transport of the particles is given by Levy flights in a quenched random potential. With a common literature model of the disorder, the random potential can only increase the rate of…
The Levy-flight dynamics can stem from simple random walks in a system whose operational time (number of steps n) typically grows superlinearly with physical time t. Thus, this processes is a kind of continuous-time random walks (CTRW),…
We consider the general branching random walk under minimal assumptions, which in particular guarantee that the empirical particle distribution admits an almost sure central limit theorem. For such a process, we study the large time decay…
We analyze a specific class of random systems that are driven by a symmetric L\'{e}vy stable noise. In view of the L\'{e}vy noise sensitivity to the confining "potential landscape" where jumps take place (in other words, to environmental…
Levy flights, characterized by the microscopic step index f, are for f<2 (the case of rare events) considered in short range and long range quenched random force fields with arbitrary vector character to first loop order in an expansion…
This paper describes the stochastic Levy--Lorentz gas driven by general long-range reference random walk on correlated and entangled random medium. Further consideration has been laid on the stochastic reinforcement of the underlying random…
In this article, the continuous time random walk on the circle is studied. We derive the corresponding generalized master equation and discuss the effects of topology, especially important when Levy flights are allowed. Then, we work out…
We propose a simple model based on the Gnedenko limit theorem for simulation and studies of the ordinary Levy motion, that is, a random process, whose increments are independent and distributed with a stable probability law. We use the…
We describe 2D gasdynamical models of jets that carry mass as well as energy to the hot gas in galaxy clusters. These flows have many attractive attributes for solving the galaxy cluster cooling flow problem: Why the hot gas temperature and…
The L\'evy walk process with rests is discussed. The jumping time is governed by an $\alpha$-stable distribution with $\alpha>1$ while a waiting time distribution is Poissonian and involves a position-dependent rate which reflects a…
The paper presents a multidimensional model for nonlinear Markovian random walks that generalizes one we developed previously (Phys. Rev. E v.79, 011110, 2009) in order to describe the Levy type stochastic processes in terms of continuous…
The Levy Walk is the process with continuous sample paths which arises from consecutive linear motions of i.i.d. lengths with i.i.d. directions. Assuming speed 1 and motions in the domain of beta-stable attraction, we prove functional limit…
Continuous time random walks combining diffusive and ballistic regimes are introduced to describe a class of L\'evy walks on lattices. By including exponentially-distributed waiting times separating the successive jump events of a walker,…
Through certain appropriate constructions, we establish periodic solutions in distribution for some stochastic differential equations with infinite-dimensional Levy noise. Additionally, we obtain the corresponding periodic measures and…
The prediction and control of rare events is an important task in disciplines that range from physics and biology, to economics and social science. The Big Jump principle deals with a peculiar aspect of the mechanism that drives rare…
The release of a gas limited by surface desorption, or by diffusion from the bulk of spherical pebbles is revisited. A method is proposed to identify the release limiting process, by comparing a partial temperature ramp, up to slightly…
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…