Related papers: Moderately Heavy Extreme Values under Extreme Long…
We investigate extreme values of Mahonian and Eulerian distributions arising from counting inversions and descents of random elements of finite Coxeter groups. To this end, we construct a triangular array of either distribution from a…
Effective field theories (EFT) parameterize the long-distance effects of short-distance dynamics whose details may or may not be known. It is known that EFT coefficients must obey certain positivity constraints if causality and unitarity…
In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…
Currently available models for spatial extremes suffer either from inflexibility in the dependence structures that they can capture, lack of scalability to high dimensions, or in most cases, both of these. We present an approach to spatial…
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…
We show that generalised extreme value statistics -the statistics of the k-th largest value among a large set of random variables- can be mapped onto a problem of random sums. This allows us to identify classes of non-identical and…
Large assemblies of nonlinear dynamical units driven by a long-wave fluctuating external field are found to generate strong turbulence with scaling properties. This type of turbulence is so robust that it persists over a finite parameter…
We analyze the largest eigenvalue statistics of m-dependent heavy-tailed Wigner matrices as well as the associated sample covariance matrices having entry-wise regularly varying tail distributions with parameter $0<\alpha<4$. Our analysis…
Quantile regression is an important tool for estimation of conditional quantiles of a response Y given a vector of covariates X. It can be used to measure the effect of covariates not only in the center of a distribution, but also in the…
We consider random vectors $X$ that satisfy the equation in law $X=AX+B$, where $A$ is a given random diagonal matrix and $B$ a given random vector, both independent of $X$. It is well known by the works of Kesten and Goldie that the…
For extreme value copulas with a known upper tail dependence coefficient we find pointwise upper and lower bounds, which are used to establish upper and lower bounds of the Spearman and Kendall correlation coefficients. We shown that in all…
Consider a random sample in the max-domain of attraction of a multivariate extreme value distribution such that the dependence structure of the attractor belongs to a parametric model. A new estimator for the unknown parameter is defined as…
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…
We consider regularly varying random vectors. Our goal is to estimate in a non-parametric way some characteristics related to conditioning on an extreme event, like the tail dependence coefficient. We introduce a quasi-spectral…
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…
Let $\mathbf{X}(n) \in \mathbb{R}^d$ be a sequence of random vectors, where $n\in\mathbb{N}$ and $d = d(n)$. Under certain weakly dependence conditions, we prove that the distribution of the maximal component of $\mathbf{X}$ and the…
There are many ways of measuring and modeling tail-dependence in random vectors: from the general framework of multivariate regular variation and the flexible class of max-stable vectors down to simple and concise summary measures like the…
The extremal characteristics of random structures, including trees, graphs, and networks, are discussed. A statistical physics approach is employed in which extremal properties are obtained through suitably defined rate equations. A variety…
Accurate modelling of the joint extremal dependence structure within a stationary time series is a challenging problem that is important in many applications.\ Several previous approaches to this problem are only applicable to certain types…
Assessing the probability of occurrence of extreme events is a crucial issue in various fields like finance, insurance, telecommunication or environmental sciences. In a multivariate framework, the tail dependence is characterized by the…