相关论文: Levy statistical fluctuations from a Random Amplif…

This paper investigates L\'evy walks with random velocities, extending classical models beyond constant speed assumptions. We derive scaling limits, demonstrating that diffusion depends on interplay between heavy-tailed duration and…

Among Markovian processes, the hallmark of L\'evy flights is superdiffusion, or faster-than-Brownian dynamics. Here we show that L\'evy laws, as well as Gaussians, can also be the limit distributions of processes with long range memory that…

L\'evy flights constitute a broad class of random walks that occur in many fields of research, from animal foraging in biology, to economy to geophysics. The recent advent of L\'evy glasses allows to study L\'evy flights in controlled way…

The passage of stars through the beam of a lensed quasar can induce violent fluctuations in its apparent brightness. The fluctuations observed in the Huchra lens, (2237+0305), are taken to be the first evidence of this ``microlensing''…

A novel model of transport is proposed to explain power law current transients and memory phenomena observed in partially ordered arrays of semiconducting nanocrystals. The model describes electron transport by a stationary Levy process of…

In optical non-linear processes rogue waves can be observed, which can be mathematically described by heavy-tailed distributions. These distributions are special due to the fact that the probability of registering extremely high intensities…

Blazars, a subset of powerful active galactic nuclei, feature relativistic jets that shine in a broadband electromagnetic radiation, e. g. from radio to TeV emission. Here I present the results of the studies that explore gamma-ray and…

The L\'evy-Lorentz gas describes the motion of a particle on the real line in the presence of a random array of scattering points, whose distances between neighboring points are heavy-tailed i.i.d. random variables with finite mean. The…

This article shows a strong averaging principle for diffusions driven by discontinuous heavy-tailed L\'evy noise, which are invariant on the compact horizontal leaves of a foliated manifold subject to small transversal random perturbations.…

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…

We discuss diffusion properties of a dynamical system, which is characterised by long-tail distributions and finite correlations. The particle velocity has the stable L\'evy distribution; it is assumed as a jumping process (the kangaroo…

We consider a dynamical system in R driven by a vector field -U', where U is a multi-well potential satisfying some regularity conditions. We perturb this dynamical system by a Levy noise of small intensity and such that the heaviest tail…

We explore the statistical behavior of the order statistics of the flights of One-sided Levy Processes (OLPs). We begin with the study of the extreme flights of general OLPs,and then focus on the class of selfsimilar processes,investigating…

We consider a random walk on one-dimensional inhomogeneous graphs built from Cantor fractals. Our study is motivated by recent experiments that demonstrated superdiffusion of light in complex disordered materials, thereby termed L\'evy…

I report a new statistical distribution formulated to confront the infamous, long-standing, computational/modeling challenge presented by highly skewed and/or leptokurtic ("fat- or heavy-tailed") data. The distribution is straightforward,…

A numerical study of the statistics of transmission ($t$) and reflection ($r$) of quasi-particles from a one-dimensional disordered lasing or amplifying medium is presented. The amplification is introduced via a uniform imaginary part in…

We analyze confining mechanisms for L\'{e}vy flights. When they evolve in suitable external potentials their variance may exist and show signatures of a superdiffusive transport. Two classes of stochastic jump - type processes are…

The non-Markovian continuous-time random walk model, featuring fat-tailed waiting times and narrow distributed displacements with a non-zero mean, is a well studied model for anomalous diffusion. Using an analytical approach, we recently…

Long tails in the velocity distribution are observed in plasmas and gravitational systems. Some experiments and observations in far-from-equilibrium conditions show that these tails behave as 1/v^(5/2). We show here that such heavy tails…

We establish distributional limit theorems for the shape statistics of a concave majorant (i.e. the fluctuations of its length, its supremum, the time it is attained and its value at $T$) of any L\'evy process on $[0,T]$ as $T\to\infty$.…