Related papers: Elementary Tail Bounds on the Hypergeometric Distr…

Let $n,k$ be positive integers such that $n\geq k$, and let $H$ be a hypergeometric random variable counting the number of black marbles in a sample without replacement of size $k$ from an urn that contains $i\in \{1,\ldots, n\}$ black and…

We introduce a ``geometric'' method to bound periods of automorphic forms. The key features of this method are the use of equidistribution results in place of mean value theorems, and the systematic use of mixing and the spectral gap.…

Kernel methods are successful approaches for different machine learning problems. This success is mainly rooted in using feature maps and kernel matrices. Some methods rely on the eigenvalues/eigenvectors of the kernel matrix, while for…

We provide an elementary proof of the lower bound for the variance of continuous unimodal distributions and obtain analogous bounds for the higher order central moments. A lower bound for the rth central moment of discrete distribution is…

We derive explicit bounds for two general classes of $L$-functions, improving and generalizing earlier known estimates. These bounds can be used, for example, to apply Turing's method for determining the number of zeros up to a given…

In this paper, a method for constructing a near optimal normal basis for algebraic extensions of a finite field is described. In each extension, except for the squares of basis elements, the product of two distinct normal basis elements can…

We investigate the relaxation of long-tailed distributions under stochastic dynamics that do not support such tails. Linear relaxation is found to be a borderline case in which long tails are exponentially suppressed in time but not…

We present bounds on the Higgs mass in the Standard Model and in the Minimal Supersymmetric Standard Model using the effective potential with next-to-leading logarithms resummed by the renormalization group equations, and physical (pole)…

We establish an upper bound on the tails of a random variable that arises as a solution of a stochastic difference equation. In the non--negative case our bound is similar to a lower bound obtained by Goldie and Gr\"ubel in 1996.

We use techniques from algebraic and extremal combinatorics to derive upper bounds on the number of independent sets in several (hyper)graphs arising from finite geometry. In this way, we obtain asymptotically sharp upper bounds for partial…

We examine the Gaussian hypergeometric beta distribution and look at the effect of having an additional term in the density kernel relative to the standard beta distribution. We reparameterise and classify this distribution into left and…

We describe how to solve the problem of Taylor dispersion in the presence of absorbing boundaries using an exact stochastic formulation. In addition to providing a clear stochastic picture of Taylor dispersion, our method leads to…

We give asymptotics for the left and right tails of the limiting Quicksort distribution. The results agree with, but are less precise than, earlier non-rigorous results by Knessl and Spankowski.

Many management decisions involve accumulated random realizations for which only the first and second moments of their distribution are available. The sharp Chebyshev-type bound for the tail probability and Scarf bound for the expected loss…

Let H = (V,E) be a k-uniform hypergraph with a vertex set V and an edge set E. Let V_p be constructed by taking every vertex in V independently with probability p. Let X be the number of edges in E that are contained in V_p. We give a…

Let (X,Y) be a bivariate elliptical random vector with associated random radius in the Gumbel max-domain of attraction. In this paper we obtain a second order asymptotic expansion of the joint survival probability P(X > x, Y> y) for x,y…

We consider distinguishing between two distribution tail models when tails of one model are lighter (or heavier) than those of the other. Two procedures are proposed: one scale-free and one location- and scale-free, and their asymptotic…

This paper presents an improved exponential tail bound for Beta distributions, refining a result in [15]. This improvement is achieved by interpreting their bound as a regular Kullback-Leibler (KL) divergence one, while introducing a…

We obtain concentration and large deviation for the sums of independent and identically distributed random variables with heavy-tailed distributions. Our concentration results are concerned with random variables whose distributions satisfy…

It is well-known that distances in random iid matrices are highly concentrated around their mean. In this note we extend this concentration phenomenon to Wigner matrices. Exponential bounds for the lower tail are also included.