Related papers: Precise large deviations for dependent subexponent…
We give necessary and sufficient conditions for two sub-vectors of a random vector with a multivariate extreme value distribution, corresponding to the limit distribution of the maximum of a multidimensional stationary sequence with…
Real space condensation is known to occur in stochastic models of mass transport in the regime in which the globally conserved mass density is greater than a critical value. It has been shown within models with factorised stationary states…
We define a class of multivariate maxima of moving multivariate maxima, generalising the M4 processes. For these stationary multivariate time series we characterise the joint distribution of extremes and compute the multivariate extremal…
We study large and moderate deviations for a life insurance portfolio, without assuming identically distributed losses. The crucial assumption is that losses are bounded, and that variances are bounded below. From a standard large…
Loynes' distribution, which characterizes the one dimensional marginal of the stationary solution to Lindley's recursion, possesses an ultimately exponential tail for a large class of increment processes. If one can observe increments but…
Employing the framework of regular variation, we propose two decompositions which help to summarize and describel high-dimensional tail dependence. Via transformation, we define a vector space on the positive orthant, yielding the notion of…
For a given one-dimensional random walk $\{S_n\}$ with a subexponential step-size distribution, we present a unifying theory to study the sequences $\{x_n\}$ for which $\mathsf{P}\{S_n>x\}\sim n\mathsf{P}\{S_1>x\}$ as $n\to\infty$ uniformly…
We develop a general technique for bounding the tail of the total variation distance between the empirical and the true distributions over countable sets. Our methods sharpen a deviation bound of Devroye (1983) for distributions over finite…
Stationary probability distributions of one-dimensional random walks on lattices with aperiodic disorder are investigated. The pattern of the distribution is closely related to the diffusional behavior, which depends on the wandering…
We establish sharp tail asymptotics for component-wise extreme values of bivariate Gaussian random vectors with arbitrary correlation between the components. We consider two scaling regimes for the tail event in which we demonstrate the…
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…
Random matrices acting on structured sets play a fundamental role in high-dimensional geometry, compressed sensing, and randomized algorithms. Existing results primarily focus on subgaussian models, when random matrices act as…
We obtain an uniform tail estimates for natural normed sums of independent random variables (r.v.) with regular varying tails of distributions. We give also many examples on order to show the exactness of offered estimates and discuss some…
The paper studies the spectral properties of large Wigner, band and sample covariance random matrices with heavy tails of the marginal distributions of matrix entries.
Large random matrices appear in different fields of mathematics and physics such as combinatorics, probability theory, statistics, operator theory, number theory, quantum field theory, string theory etc... In the last ten years, they…
The sums and maxima of non-stationary random length sequences of regularly varying random variables may have the same tail and extremal indices, Markovich and Rodionov (2020). The main constraint is that there exists a unique series in a…
We study large deviations for random walks on Lie groups defined by $\sigma_n^n = \exp(\frac1nX_1)\cdots\exp(\frac1nX_n)$, where $\{X_n\}_{n\geq1}$ is an i.i.d sequence of bounded random variables in the Lie algebra $\mathfrak{g}$. We…
We conjecture an explicit expression for the lower tail large deviation rate function of the partition function of the log-Gamma polymer. We rigorously prove our result, except for one step for which we only provide heuristic evidence. We…
The analysis of extremal dependence in high dimensions has recently attracted considerable interest. Existing methodology primarily focuses on modeling and estimation of extremal dependence structures, often supported by concentration…
The probability and structure of co-occurrences of extreme values in multivariate data may critically depend on auxiliary information provided by covariates. In this contribution, we develop a flexible generalized additive modeling…