Related papers: Large Deviations of Bivariate Gaussian Extrema

Causal discovery in multivariate extremes is challenging because extreme observations are sparse, dependent, and often affected by latent common shocks. Existing approaches focus on undirected extremal dependence, require prior graph…

We obtain asymptotic bounds for the tail distribution of steady-state waiting time in a two server queue where each server processes incoming jobs at a rate equal to the rate of their arrivals (that is, the half-loaded regime). The job…

We examine a distributional fixed-point equation related to a multi-type branching process that is key in the cluster sizes analysis of multivariate heavy-tailed Hawkes processes. Specifically, we explore the tail behavior of its solution…

The skew-normal and related families are flexible and asymmetric parametric models suitable for modelling a diverse range of systems. We show that the multivariate maximum of a high-dimensional extended skew-normal random sample has…

In this paper we are concerned with the analysis of heavy-tailed data when a portion of the extreme values is unavailable. This research was motivated by an analysis of the degree distributions in a large social network. The degree…

We derive exact asymptotics of $$\mathbb{P}\left(\sup_{\mathbf{t}\in {\mathcal{A}}}X(\mathbf{t})>u\right),~ \text{as}~ u\to\infty,$$ for a centered Gaussian field $X(\mathbf{t}),~ \mathbf{t}\in \mathcal{A}\subset\mathbb{R}^n$, $n>1$ with…

Whether an extreme observation is an outlier or not, depends strongly on the corresponding tail behaviour of the underlying distribution. We develop an automatic, data-driven method to identify extreme tail behaviour that deviates from the…

Various natural phenomena exhibit spatial extremal dependence at short spatial distances. However, existing models proposed in the spatial extremes literature often assume that extremal dependence persists across the entire domain. This is…

In this paper, we compute multivariate tail risk probabilities where the marginal risks are heavy-tailed and the dependence structure is a Gaussian copula. The marginal heavy-tailed risks are modeled using regular variation which leads to a…

We prove an exponential probability tail inequality for positive semidefinite quadratic forms in a subgaussian random vector. The bound is analogous to one that holds when the vector has independent Gaussian entries.

These notes were written for the mini-course "Extrema of log-correlated random variables: Principles and Examples" at the Introductory School held in January 2015 at the Centre International de Rencontres Math\'ematiques in Marseille. There…

In this paper, we obtain some results on precise large deviations for non-random and random sums of widely dependent random variables with common dominatedly varying tail distribution or consistently varying tail distribution on…

Identifying groups of variables that may be large simultaneously amounts to finding out which joint tail dependence coefficients of a multivariate distribution are positive. The asymptotic distribution of a vector of nonparametric,…

The extreme values theory presents specific tools for modeling and predicting extreme phenomena. In particular, risk assessment is often analyzed through measures for tail dependence and high values clustering. Despite technological…

The masses of data now available have opened up the prospect of discovering weak signals using machine-learning algorithms, with a view to predictive or interpretation tasks. As this survey of recent results attempts to show, bringing…

This paper addresses heavy-tailed large deviation estimates for the distribution tail of functionals of a class of spectrally one-sided L\'evy process. Our contribution is to show that these estimates remain valid in a near-critical regime.…

We propose a variational tail bound for norms of random vectors under moment assumptions on their one-dimensional marginals. A simplified version of the bound that parametrizes the ``aggregating distribution'' using a certain pushforward of…

Let $M_n$ be the maximum of $n$ zero-mean gaussian variables $X_1,..,X_n$ with covariance matrix of minimum eigenvalue $\lambda$ and maximum eigenvalue $\Lambda$. Then, for $n \ge 70$, $$\Pr\{M_n \ge \lambda \left (2 \log n - 2.5 - \log(2…

We establish precise upper-tail asymptotics and large deviation principles for the rightmost eigenvalue $\lambda_1$ of Wigner matrices with sub-Gaussian entries. In contrast to the case of heavier tails, where deviations of $\lambda_1$ are…

The term moderate deviations is often used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between a convergence in probability of some random variables to a constant and a weak convergence…