Related papers: Global fluctuations in physical systems: a subtle …
A formula to calculate the quantum fluctuations of energy in small subsystems of a hot and relativistic gas is derived. We find an increase in fluctuations for subsystems of small sizes, but we agrees with the energy fluctuations in the…
Extreme value analysis is an essential methodology in the study of rare and extreme events, which hold significant interest in various fields, particularly in the context of environmental sciences. Models that employ the exceedances of…
When passing from the univariate to the multivariate setting, modelling extremes becomes much more intricate. In this introductory exposition, classical multivariate extreme value theory is presented from the point of view of multivariate…
Inspired by the importance of inhibitory and excitatory couplings in the brain, we analyze the largest eigenvalue statistics of random networks incorporating such features. We find that the largest real part of eigenvalues of a network,…
The financial losses from extreme weather events can have a disastrous effect, often costing billions of pounds. While changes in the disposition of individual events is of importance to both the insurance and re-insurance industries, these…
We discuss maximum entangled states of quantum systems in terms of quantum fluctuations of all essential measurements responsible for manifestation of entanglement. Namely, we consider maximum entanglement as a property of states, for which…
The univariate extreme value theory deals with the convergence in type of powers of elements of sequences of cumulative distribution functions on the real line when the power index gets infinite. In terms of convergence of random variables,…
Extreme value (EV) statistics of correlated systems are widely investigated in many fields, spanning the spectrum from weather forecasting to earthquake prediction. Does the unavoidable discrete sampling of a continuous correlated…
We present a novel statistical treatment, the "metastatistics of extreme events", for calculating the frequency of extreme events. This approach, which is of general validity, is the proper statistical framework to address the problem of…
We give conditions to prove the existence of an Extremal Index for general stationary stochastic processes by detecting the presence of one or more underlying periodic phenomena. This theory, besides giving general useful tools to identify…
This article proposes a generalized notion of extreme multivariate dependence between two random vectors which relies on the extremality of the cross-covariance matrix between these two vectors. Using a partial ordering on the…
A generic physical situation is considered where Im $\Pi$, the imaginary part of polarization operator (generalized susceptibility), can be measured on a finite interval and the high frequency asymptotics (up to a few orders) of $\Pi$ can…
Extreme values modeling has attracting the attention of researchers in diverse areas such as the environment, engineering, or finance. Multivariate extreme value distributions are particularly suitable to model the tails of multidimensional…
We derive a formula that defines quantum fluctuations of energy in subsystems of a hot relativistic gas. For small subsystem sizes we find substantial increase of fluctuations compared to those known from standard thermodynamic…
The large scale distribution of galaxies in the universe displays a complex pattern of clusters, super-clusters, filaments and voids with sizes limited only by the boundaries of the available samples. A quantitative statistical…
We extend the scope of the dynamical theory of extreme values to cover phenomena that do not happen instantaneously, but evolve over a finite, albeit unknown at the onset, time interval. We consider complex dynamical systems, composed of…
A plethora of natural, artificial and social systems exist which do not belong to the Boltzmann-Gibbs (BG) statistical-mechanical world, based on the standard additive entropy $S_{BG}$ and its associated exponential BG factor. Frequent…
We extend the Exchange Fluctuation Theorem for energy exchange between thermal quantum systems beyond the assumption of molecular chaos, and describe the non-equilibrium exchange dynamics of correlated quantum states. The relation…
We argue that the transition to turbulence is controlled by large amplitude events that follow extreme distribution theory. The theory suggests an explanation for recent observations of the turbulent state lifetime which exhibit…
The statistical mechanical basis of the fluctuation theory of mixtures is reviewed. An overview of the statistical mechanical relations between the microscopic properties of a system and its macroscopic properties is presented. The…