Related papers: Do we observe L\'evy flights in cosmic rays?
A L\'evy random medium, in a given space, is a random point process where the distances between points, a.k.a. targets, are long-tailed. Random walks visiting the targets of a L\'evy random medium have been used to model many (physical,…
Via a Bayesian likelihood analysis using 219 recent cosmic ray spectral data points we extract the anomalous part of the cosmic $e^\pm$ flux. First we show that a significant tension exists between the $e^\pm$ related and the rest of the…
The distribution of arrival directions of cosmic rays is remarkably isotropic, which is a consequence of their repeated scattering in magnetic fields. Yet, high-statistics observatories like IceCube and HAWC have revealed the presence of…
We review some of the theory relevant to passage times of one-dimensional L\'evy processes out of bounded regions, highlighting results that are useful in physical phenomena modelled by heavy-tailed L\'evy flights. The process is…
Theoretical predictions for lateral distribution function of electrons in extensive air showers based on scaling formalism are presented. Our results are tested by comparison with AGASA experimental data taking into account the contribution…
The measurement of the anisotropy in the arrival direction of cosmic rays is complementary to the study of their energy spectrum and chemical composition to understand their origin and propagation. It is also a tool to probe the structure…
We consider an infinitely divisible random field indexed by $\mathbb{R}^d$, $d\in\mathbb{N}$, given as an integral of a kernel function with respect to a L\'evy basis with a L\'evy measure having a regularly varying right tail. First we…
A new conceptual approach for examining the origin of cosmic rays is developed by considering the characteristics of particle trajectory distributions in four-dimensional Euclidean space-time. Transformation of an isotropic distribution…
The origin of galactic cosmic rays is one of the most interesting unsolved problems in astroparticle physics. Experimentally, the problem is attacked by a multi-disciplinary effort, namely by direct measurements of cosmic rays above the…
Rayleigh-L\'evy flights are simplified cosmological tools which capture certain essential statistical properties of the cosmic density field, including hierarchical structures in higher-order correlations, making them a valuable reference…
Recent studies have shown that the anisotropy is of great value to decipher cosmic rays' origin and propagation. We have built an unified scenario to describe the observations of the energy spectra and the large-scale anisotropy and called…
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…
Lévy flights in steeper than harmonic potentials have been shown to exhibit finite variance and a critical time at which a bifurcation from an initial mono-modal to a terminal bimodal distribution occurs (Chechkin et al., Phys. Rev. E…
The L\'evy, jumping process, defined in terms of the jumping size distribution and the waiting time distribution, is considered. The jumping rate depends on the process value. The fractional diffusion equation, which contains the variable…
Cosmic rays, along with stellar radiation and magnetic fields, are known to make up a significant fraction of the energy density of galaxies such as the Milky Way. When cosmic rays interact in the interstellar medium, they produce gamma-ray…
A review is given of the main properties of the charged component of galactic cosmic rays, particles detected at Earth with an energy spanning from tens of MeV up to about 10^19 eV. After a short introduction to the topic and an historical…
The 320 EeV air shower detected by the Fly's Eye poses an important problem. Careful analysis of pathlength limitations for the possible particle types due to cosmic background radiation verifies that the particle very likely traveled less…
We consider a generalization of a one-dimensional stochastic process known in the physical literature as L\'evy-Lorentz gas. The process describes the motion of a particle on the real line in the presence of a random array of marked points,…
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…
The origin of cosmic rays is one of the major unresolved questions in astrophysics. In particular, the highest energy cosmic rays observed possess macroscopic energies and their origin is likely associated with the most energetic processes…