Related papers: Do we observe L\'evy flights in cosmic rays?
The reflected process of a random walk or L\'evy process arises in many areas of applied probability, and a question of particular interest is how the tail of the distribution of the heights of the excursions away from zero behaves…
We briefly review sources of cosmic rays, their composition and spectra as well as their propagation in the galactic and extragalactic magnetic fields, both regular and fluctuating. A special attention is paid to the recent results of the…
Diffuse emission in gamma-rays and neutrinos are produced by the interaction of cosmic rays with the interstellar medium. Below some hundreds of TeV, the sources of these cosmic rays are most likely Galactic. Hence, observations of…
High-energy cosmic rays, impinging on the atmosphere of the Earth initiate cascades of secondary particles, the extensive air showers. The electrons and positrons in the air shower emit electromagnetic radiation. This emission is detected…
Cosmic rays up to at least PeV energies are usually described in the framework of an elementary scenario that involves acceleration by objects that are located in the disk of the Milky Way, such as supernova remnants or massive star-forming…
From the analysis of AGASA data above $4 \times 10^{19}$ eV, we show that the ultra-high energy cosmic rays flux is neither purely isotropic, nor reflects the expected anisotropy from a pure source distribution that maps large scale…
Arrival directions of cosmic rays with the energy E>4.10^19 eV are analyzed on the basis of the Yakutsk and AGASA extensive air shower arrays. It is supposed that the clusters can be formed as a result of fragmentation of superheavy nuclei.…
Important observational results have been recently reported on the angular distributions of cosmic rays at all energies, calling into question the perception of cosmic rays a decade ago. These results together with their in-progress…
Three pairs of possibly correlated ultra-high energy cosmic ray events were reported by Hayashida et al (1996). Here we calculate the propagation of the corresponding particles through both the intergalactic and galactic magnetic fields.…
The latest results from PAMELA and FERMI experiments confirm the necessity to improve theoretical models of production and propagation of galactic electrons and positrons. There are many possible explanations for the positron excess…
Comb geometry, constituted of a backbone and fingers, is one of the most simple paradigm of a two dimensional structure, where anomalous diffusion can be realized in the framework of Markov processes. However, the intrinsic properties of…
Very recently, a possible clustering of a subset of observed ultrahigh energy cosmic rays above about 40EeV (4x10^19eV) in pairs near the supergalactic plane was reported. We show that a confirmation of this effect would provide information…
Probability distributions defined on the half space are known to be quite different from those in the full space. Here, a nonextensive entropic treatment is presented for the half space in an analytic and self-consistent way. In this…
The distribution of arrival directions of ultra-high energy cosmic rays may yield clues to their mysterious origin. We introduce a method of {\it invariant statistics} to analyze cosmic ray data which eliminates coordinate-dependent…
Research in cosmic rays is now nearly a century old, but most of the fundamental questions in this field remain unanswered, on the other hand the perspectives of future studies in the next decade are very bright. New detectors will provide…
We provide theoretical and experimental evidence of statistical outliers in random laser emission that are not accounted for by the, now established, power-law tailed (L\'evy) distribution. Such outliers manifest themselves as single, large…
We investigate the injection spectrum of ultra-high-energy (>10^{15} eV) cosmic rays under the hypotheses that (1) these cosmic rays are protons and (2) the sources of these cosmic rays are extra-galactic and are homogeneously distributed…
Levy flights are random walks in which the probability distribution of the step sizes is fat-tailed. Levy spatial diffusion has been observed for a collection of ultra-cold Rb atoms and single Mg+ ions in an optical lattice. Using the…
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 arguments surrounding the Galactic component of the cosmic rays, the energy budget, questions of composition, spectral features, anisotropy, sources etc, will be critically examined. We are moving into a new phase in the study of the…