相关论文: Extreme value statistics and the Pareto distributi…
We show that fluctuations of Raman amplified pulses, in the presence of a noisy pump, follow extreme value statistics, and provide mathematical insight into the origin of this perplexing behavior.
Extreme events appear in many physics phenomena, whenever the probability distribution has a ''heavy tail'', differing very much from the equilibrium one. Most unusual are the cases of power-law (Pareto) probability distributions. Among…
We investigate the statistical properties of the extreme events of the solar cycle as measured by the sunspot number. The recent advances in the methodology of the theory of extreme values is applied to the maximal extremes of the time…
In this article we show the relationship between the Pareto distribution and the gamma distribution. This shows that the second one, appropriately extended, explains some anomalies that arise in the practical use of extreme value theory.…
A stochastic model for intermittent fluctuations due to a super-position of uncorrelated Lorentzian pulses is presented. For constant pulse duration, this is shown to result in an exponential power spectral density for the stationary…
Most extreme events in real life can be faithfully modeled as random realizations from a Generalized Pareto distribution, which depends on two parameters: the scale and the shape. In many actual situations, one is mostly concerned with the…
Extreme value statistics, or extreme statistics for short, refers to the statistics that characterizes rare events of either unusually high or low intensity: climate disasters like floods following extremely intense rains are among the…
We study rare events in the extreme value statistics of stochastic symmetric jump processes with power tails in the distributions of the jumps, using the big-jump principle. The principle states that in the presence of stochastic processes…
We consider two mean-field models of structural glasses, the random energy model (REM) and the $p$-spin model (PSM), and we show that the finite-size fluctuations of the freezing temperature are described by extreme-value statistics (EVS)…
Properties of random and fluctuating systems are often studied through the use of Gaussian distributions. However, in a number of situations, rare events have drastic consequences, which can not be explained by Gaussian statistics.…
The statistics of natural catastrophes contains very counter-intuitive results. Using earthquakes as a working example, we show that the energy radiated by such events follows a power-law or Pareto distribution. This means, in theory, that…
When light travels through strongly scattering media with optical gain, the synergy between diffusive transport and stimulated emission can lead to lasing action. Below the threshold pump power, the emission spectrum is smooth and…
Pulse splitting is a crucial and common process in nonlinear fiber optics. When an intense laser pulse is launched into a highly nonlinear fiber, a stream of fundamental solitons is generated, their temporal separations increasing during…
The interplay of such cornerstones of modern nonlinear fiber optics as a nonlinearity, stochasticity and polarization leads to variety of the noise induced instabilities including polarization attraction and escape phenomena harnessing of…
The issue of speckle statistics from ultrasound images of soft tissues such as the liver has a long and rich history. A number of theoretical distributions, some related to random scatterers or fades in optics and radar, have been…
Radiative transfer equations are derived and solved for the stimulated Raman scattering of water maser lines in the astrophysical plasmas with electron density of about 10^6 - 10^7 cm-3. In stimulated Raman scattering, the energy of water…
Fluctuations due to a super-position of uncorrelated Lorentzian pulses with a random distribution of amplitudes and duration times are considered. These are demonstrated to be strongly intermittent in the limit of weak pulse overlap,…
Based upon the rate equations for the photon distribution function obtained in the previous paper, we study the inverse Compton scattering process for high-energy nonthermal electrons. Assuming the power-law electron distribution, we find a…
We show that the probability of appearance of synchronisation in chaotic coupled map lattices is related to the distribution of the maximum of a certain observable evaluated along almost all orbit. We show that such distribution belongs to…
Numerous approaches are proposed in the literature for non-stationarity marginal extreme value inference, including different model parameterisations with respect to covariate, and different inference schemes. The objective of this article…