Related papers: Statistics of Extreme Values in Time Series with I…
We show that time-correlation functions of arbitrary order for any random variable in a statistical dynamical system can be calculated as higher-order response functions of the mean history of the variable. The response is to a ``control…
Fluctuations in the return time statistics of a dynamical system can be described by a new spectrum of dimensions. Comparison with the usual multifractal analysis of measures is presented, and difference between the two corresponding sets…
Extreme value statistics (EVS) concerns the study of the statistics of the maximum or the minimum of a set of random variables. This is an important problem for any time-series and has applications in climate, finance, sports, all the way…
The Extremal Index is a parameter that measures the intensity of clustering of rare events and is usually equal to the reciprocal of the mean of the limiting cluster size distribution. We show how to build dynamically generated stochastic…
We present a study of the intermittent properties of a shell model of turbulence with unprecedented statistics, about $\sim 10^7$ eddy turn over time, achieved thanks to an implementation on a large-scale parallel GPU factory. This allows…
We study the statistical properties of return intervals $r$ between successive energy dissipation rates above a certain threshold $Q$ in three-dimensional fully developed turbulence. We find that the distribution function $P_Q(r)$ scales…
We consider renewal processes where events, which can for instance be the zero crossings of a stochastic process, occur at random epochs of time. The intervals of time between events, $\tau_{1},\tau_{2},...$, are independent and identically…
We consider discrete time dynamical systems and show the link between Hitting Time Statistics (the distribution of the first time points land in asymptotically small sets) and Extreme Value Theory (distribution properties of the partial…
It is well-known that the expected scaled maximum of non-negative random variables with unit mean defines a stable tail dependence function associated with some extreme-value copula. In the special case when these random variables are…
Fluctuations of observables as functions of time, or "fluctuation patterns", are studied in a chaotic microscopically reversible system that has irreversibly reached a nonequilibrium stationary state. Supposing that during a certain, long…
Fractal time series has been shown to be self-affine and are characterized by a roughness exponent H. The exponent H is a measure of the persistence of the fluctuations associated with the time series. We use a recently introduced method…
On the occasion of Laurens de Haan's 70th birthday, we discuss two aspects of the statistical inference on the extreme value behavior of time series with a particular emphasis on his important contributions. First, the performance of a…
Detecting anomalies in a temporal sequence of graphs can be applied is areas such as the detection of accidents in transport networks and cyber attacks in computer networks. Existing methods for detecting abnormal graphs can suffer from…
The correlation properties of the nonaffine elastic response in strongly disordered materials are investigated using the theory of correlated random matrices and supported by numerical models. While the nonaffine displacement field itself…
We introduce the extremal range, a local statistic for studying the spatial extent of extreme events in random fields on $\mathbb{R}^d$. Conditioned on exceedance of a high threshold at a location $s$, the extremal range at $s$ is the…
Thermal or finite-size scaling analyses of importance sampling Monte Carlo time series in the vicinity of phase transition points often combine different estimates for the same quantity, such as a critical exponent, with the intent to…
The accurate estimation of scaling exponents is central in the observational study of scale-invariant phenomena. Natural systems unavoidably provide observations over restricted intervals; consequently a stationary stochastic process (time…
We are interested in investigating the statistical properties of extreme values for strongly correlated variables. The starting motivation is to understand how the strong-correlation properties of power-law distributed processes affect the…
We investigate extreme value theory of a class of random sequences defined by the all-time suprema of aggregated self-similar Gaussian processes with trend. This study is motivated by its potential applications in various areas and its…
We study fluctuations in diffusion-limited reaction systems driven out of their stationary state. Using a numerically exact method, we investigate fluctuation ratios in various systems which differ by their level of violation of microscopic…