Related papers: Power-law tail distributions and nonergodicity
The nature of diffusion is usually studied for particles or time-evolving systems. Similar in principle, such studies can be conducted by tracking how a given function of observable properties evolves over time-akin to the evolution of…
One of the first steps to understand and forecast economic downturns is identifying their frequency distribution, but it remains uncertain. This problem is common in phenomena displaying power-law-like distributions. Power laws play a…
We study the stochastic behavior of heterogeneous diffusion processes with the power-law dependence $D(x)\sim|x|^{\alpha}$ of the generalized diffusion coefficient encompassing sub- and superdiffusive anomalous diffusion. Based on…
By a natural nonextensive generalization of the conservation of energy in the q-kinetic theory, we study the nonextensivity and the power-law distributions for the many-body systems with the self-gravitating long-range interactions. It is…
Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is…
Statistical description of stochastic dynamics in highly unstable potentials is strongly affected by properties of divergent trajectories, that quickly leave meta-stable regions of the potential landscape and never return. Using ideas from…
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…
The derivation of the maximum entropy distribution of particles in boxes yields two kinds of distributions: a "bell-like" distribution and a long-tail distribution. The first one is obtained when the ratio between particles and boxes is…
This paper quantifies the ergodicity and the rate of decay of the tail of the stationary distribution for a broad class of storage models, encompassing constant, linear, and power-type release rates with both finite and infinite activity…
Starting from the BBGKY hierarchy, describing the kinetics of nonlinear particle system, we obtain the relevant entropy and stationary distribution function. Subsequently, by employing the Lorentz transformations we propose the relativistic…
The different between the inverse power function and the negative exponential function is significant. The former suggests a complex distribution, while the latter indicates a simple distribution. However, the association of the power-law…
We examine random variables in the power law/regularly varying class with stochastic tail exponent, the exponent $\alpha$ having its own distribution. We show the effect of stochasticity of $\alpha$ on the expectation and higher moments of…
Localized rain events have been found to follow power-law distributions over several decades, suggesting parallels between precipitation and seismic activity [O. Peters et al., PRL 88, 018701 (2002)]. Similar power laws can be generated by…
The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is then regarded as a first-return random walk…
We examine whether the principle of detailed balance holds for the power-law distributions generated from the general Langevin equation under the generalized fluctuation-dissipation relation (FDR). With the detailed balance and the…
Using the joint distribution for proper time-delays of a chaotic cavity derived by Brouwer, Frahm & Beenakker [Phys. Rev. Lett. {\bf 78}, 4737 (1997)], we obtain, in the limit of large number of channels $N$, the large deviation function…
Inhomogeneous temporal processes, like those appearing in human communications, neuron spike trains, and seismic signals, consist of high-activity bursty intervals alternating with long low-activity periods. In recent studies such bursty…
We consider diffusion processes with a spatially varying diffusivity giving rise to anomalous diffusion. Such heterogeneous diffusion processes are analysed for the cases of exponential, power-law, and logarithmic dependencies of the…
Time averages extracted from single-particle trajectories in complex media often vary strongly from one trajectory to another, even for long measurement times. Such persistent trajectory-to trajectory scatter is commonly observed in…
We find a general formula for the distribution of time-averaged observables for systems modeled according to the sub-diffusive continuous time random walk. For Gaussian random walks coupled to a thermal bath we recover ergodicity and…