Related papers: A Sharp Gaussian Tail Bound for Sums of Uniforms

In this paper we present various new inequalities for tail proabilities for distributions that are elements of the most improtant exponential families. These families include the Poisson distributions, the Gamma distributions, the binomial…

This contribution establishes exact tail asymptotics of $\sup_{(s,t)\in\mathbf{E}}$ $X(s,t)$ for a large class of nonhomogeneous Gaussian random fields $X$ on a bounded convex set $\mathbf{E}\subset\mathbb{R}^2$, with variance function that…

We investigate a way of comparing and classifying tails of random variables. Our approach extends the notion of classical indices, such as exponential and moment indices, which are widely used measuring heaviness of tail functions. A…

We propose an analytical approach to the computation of tail probabilities of compound distributions whose individual components have heavy tails. Our approach is based on the contour integration method, and gives rise to a representation…

We prove a dimension-free tail comparison between the Euclidean norms of sums of independent random vectors uniformly distributed in centred Euclidean spheres and properly rescaled standard Gaussian random vectors.

This paper focuses on rare events associated with the tail probabilities of the extremal eigenvalues in the $\beta$-Jacobi ensemble, which plays a critical role in both multivariate statistical analysis and statistical physics. Under the…

For a distribution $F^{*\tau}$ of a random sum $S_{\tau}=\xi_1+...+\xi_{\tau}$ of i.i.d. random variables with a common distribution $F$ on the half-line $[0,\infty)$, we study the limits of the ratios of tails…

The aim of this paper is to give a precise asymptotic description of some eigenvalue statistics stemming from random matrix theory. More precisely, we consider random determinants of the GUE, Laguerre, Uniform Gram and Jacobi beta ensembles…

The paper contains results in three areas: First we present a general estimate for tail probabilities of Gaussian quadratic forms with known expectation and variance. Thereafter we analyze the distribution of norms of complex Gaussian…

We present two-sided estimates of moments and tails of polynomial chaoses of order at most three generated by independent symmetric random variables with log-concave tails as well as for chaoses of arbitrary order generated by independent…

We provide sharp bounds for the exponential moments and $p$-moments, $1\leqslant p \leqslant 2$, of the terminate distribution of a martingale whose square function is uniformly bounded by one. We introduce a Bellman function for the…

The tail behavior of aggregates of heavy-tailed random vectors is known to be determined by the so-called principle of "one large jump'', be it for finite sums, random sums, or, L\'evy processes. We establish that, in fact, a more general…

We consider the probability that a weighted sum of $n$ i.i.d. random variables $X_j$, $j = 1, . . ., n$, with stretched exponential tails is larger than its expectation and determine the rate of its decay, under suitable conditions on the…

Handling multiplicity without losing much power has been a persistent challenge in various fields that often face the necessity of managing numerous statistical tests simultaneously. Recently, $p$-value combination methods based on…

Consider $n$ real/complex, independent/dependent random variables with respective tail bounds and $g$ a measurable function of the r.v.'s. Consider $f$ the "sharpest" tail bound of $g$ (sharpest in the sense that if $f$ were any less, then…

Consider an expander graph in which a $\mu$ fraction of the vertices are marked. A random walk starts at a uniform vertex and at each step continues to a random neighbor. Gillman showed in 1993 that the number of marked vertices seen in a…

We consider the sums $S_n=\xi_1+\cdots+\xi_n$ of independent identically distributed random variables. We do not assume that the $\xi$'s have a finite mean. Under subexponential type conditions on distribution of the summands, we find the…

Concentration inequalities form an essential toolkit in the study of high dimensional (HD) statistical methods. Most of the relevant statistics literature in this regard is based on sub-Gaussian or sub-exponential tail assumptions. In this…

We obtain new upper tail probabilities of $m$-times integrated Brownian motions under the uniform norm and the $L^p$ norm. For the uniform norm, Talagrand's approach is used, while for the $L^p$ norm, Zolotare's approach together with…

We introduce a new class of heavy-tailed distributions for which any weighted average of independent and identically distributed random variables is larger than one such random variable in (usual) stochastic order. We show that many…