Related papers: Sharp upper tail behavior of line ensembles via th…

Let $Y=\sum_{k\ge 1} 1_{A_k}$ be an infinite sum of the indicators of independent events. We investigate a precise (as opposed to logarithmic) first-order asymptotic behavior of the tail probabilities $\mathbb{P}\{Y\ge n\}$ and the point…

We consider the elliptic Ginibre ensembles in the real, complex and symplectic symmetry classes. As the matrix size tends to infinity, we derive the asymptotic behaviour of the upper tail large deviation probabilities for both the spectral…

We develop a probabilistic method for assessing the tail behavior and geometric stability of one-dimensional n i.i.d. samples by tracking how their span contracts when the most extreme points are trimmed. Central to our approach is the…

For models in the KPZ universality class, such as the zero temperature model of planar last passage-percolation (LPP) and the positive temperature model of directed polymers, its upper tail behavior has been a topic of recent interest, with…

We develop an efficient simulation algorithm for computing the tail probabilities of the infinite series $S = \sum_{n \geq 1} a_n X_n$ when random variables $X_n$ are heavy-tailed. As $S$ is the sum of infinitely many random variables, any…

We prove tail estimates for variables $\sum_i f(X_i)$, where $(X_i)_i$ is the trajectory of a random walk on an undirected graph (or, equivalently, a reversible Markov chain). The estimates are in terms of the maximum of the function $f$,…

We develop a black-box theory, which can be used to show that a sequence of Gibbsian line ensembles is tight, provided that the one-point marginals of the lowest labeled curves of the ensembles are tight and globally approximate an inverted…

The extremal tail probabilities of moving sums in a marked Poisson random field is examined here. These sums are computed by adding up the weighted occurrences of events lying within a scanning set of fixed shape and size. Change of measure…

We study the upper tail of the number of arithmetic progressions of a given length in a random subset of {1,...,n}, establishing exponential bounds which are best possible up to constant factors in the exponent. The proof also extends to…

The non-asymptotic tail bounds of random variables play crucial roles in probability, statistics, and machine learning. Despite much success in developing upper bounds on tail probability in literature, the lower bounds on tail…

The extreme value theory is very popular in applied sciences including Finance, economics, hydrology and many other disciplines. In univariate extreme value theory, we model the data by a suitable distribution from the general max-domain of…

We study the asymptotic behaviour of widely used tests for evaluating and comparing predictive accuracy when forecast errors exhibit heavy tails. In particular, when loss differentials have infinite variance, the Diebold-Mariano test…

In many applied fields, the prediction of more severe events than those already recorded is crucial for safeguarding against potential future calamities. What-if analyses, which evaluate hypothetical scenarios up to the worst-case event,…

Modern statistical analyses often encounter datasets with massive sizes and heavy-tailed distributions. For datasets with massive sizes, traditional estimation methods can hardly be used to estimate the extreme value index directly. To…

We prove new lower bounds for the upper tail probabilities of suprema of Gaussian processes. Unlike many existing bounds, our results are not asymptotic, but supply strong information when one is only a little into the upper tail. We…

We derive PAC-Bayesian learning guarantees for heavy-tailed losses, and obtain a novel optimal Gibbs posterior which enjoys finite-sample excess risk bounds at logarithmic confidence. Our core technique itself makes use of PAC-Bayesian…

Models for extreme values are generally derived from limit results, which are meant to be good enough approximations when applied to finite samples. Depending on the speed of convergence of the process underlying the data, these…

We present a method for upper and lower bounding the right and the left tail probabilities of continuous random variables (RVs). For the right tail probability of RV $X$ with probability density function $f (x)$, this method requires first…

We present a systematic short time expansion for the generating function of the one point height probability distribution for the KPZ equation with droplet initial condition, which goes much beyond previous studies. The expansion is checked…

We introduce a new type of estimator for the spectral tail process of a regularly varying time series. The approach is based on a characterizing invariance property of the spectral tail process, which is incorporated into the new estimator…