Related papers: Relativistic kinetics and power-law tailed distrib…
Experimental particle spectra can be successfully described by power-law tailed energy distributions characteristic to canonical equilibrium distributions associated to R\'enyi's or Tsallis' entropy formula - over a wide range of energies,…
A stationary distribution function that describes the entire processes of propagation of relativistic particles, including the transition between the ballistic and diffusion regimes, is obtained. The spacial component of the constructed…
In relativistic kinetic theory, which underlies relativistic hydrodynamics, the molecular chaos hypothesis stands at the basis of the equilibrium Maxwell-Juttner probability distribution for the four-momentum $p^{\alpha}$. We investigate…
Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get…
A procedure for loading particle velocities from a relativistic kappa distribution in particle-in-cell (PIC) and Monte Carlo simulations is presented. It is based on the rejection method and the beta prime distribution. The rejection part…
Most astrophysical plasmas are observed to have velocity distribution functions exhibiting non-Maxwellian suprathermal tails. The high energy particle populations are accurately represented by the family of kappa-distributions where the use…
Studies of collective human behavior in the social sciences, often grounded in details of actions by individuals, have much to offer `social' models from the physical sciences concerning elegant statistical regularities. Drawing on…
Stochastic models, based on random processes, may lead to power law distributions, which provide long range correlations. The observation of power law behavior and the presence of long range correlations in biological systems has been…
Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get…
Power-law tails are ubiquitous in income distributions and in the energy distributions of diluted relativistic gases. We analyze the conceptual link between these two cases. In economic interactions fat tails arise because the richest…
This Colloquium reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since the late 1990s. By analogy with the Boltzmann-Gibbs distribution of energy in physics, it is shown that…
We discuss a relativistic diffusion in the proper time in an approach of Schay and Dudley. We derive (Langevin) stochastic differential equations in various coordinates.We show that in some coordinates the stochastic differential equations…
Empirical evidence shows stock returns are often heavy-tailed rather than normally distributed. The $\kappa$-generalised distribution, originated in the context of statistical physics by Kaniadakis, is characterised by the…
A mechanism is proposed for the appearance of power law distributions in various complex systems. It is shown that in a conservative mechanical system composed of subsystems with different numbers of degrees of freedom a robust power-law…
Probability distributions having power-law tails are observed in a broad range of social, economic, and biological systems. We describe here a potentially useful common framework. We derive distribution functions $\{p_k\}$ for situations in…
Kappa distributions are widely used in space plasma physics to model velocity distribution functions with heavy tails. Parameter estimation in these distributions is, however, complicated by the fact that the kappa distribution does not…
We review briefly the concepts underlying complex systems and probability distributions. The later are often taken as the first quantitative characteristics of complex systems, allowing one to detect the possible occurrence of regularities…
Starting from the generalized exponential function $\exp_{\kappa}(x)=(\sqrt{1+\kappa^{2}x^{2}}+\kappa x)^{1/\kappa}$, with $\exp_{0}(x)=\exp(x)$, proposed in Ref. [G. Kaniadakis, Physica A \textbf{296}, 405 (2001)], the survival function…
To know the statistical distribution of a variable is an important problem in management of resources. Distributions of the power law type are observed in many real systems. However power law distributions have an infinite variance and thus…
Heavy-tailed or power-law distributions are becoming increasingly common in biological literature. A wide range of biological data has been fitted to distributions with heavy tails. Many of these studies use simple fitting methods to find…