Related papers: Tight Chernoff-Like Bounds Under Limited Independe…
We study the Hardy inequality when the singularity is placed on the boundary of a bounded domain in $\mathbb{R}^n$ that satisfies both an interior and exterior ball condition at the singularity. We obtain the sharp Hardy constant $n^2/4$ in…
We establish upper and lower bounds with matching leading terms for tails of weighted sums of two-sided exponential random variables. This extends Janson's recent results for one-sided exponentials.
Quantile aggregation with dependence uncertainty has a long history in probability theory with wide applications in finance, risk management, statistics, and operations research. Using a recent result on inf-convolution of quantile-based…
We give sharp bounds for the reliability measure of a discrete r.v. defined on {0, ..., n}, conditionally on the knowledge of the first three moments of the r.v. The present work is as an extension of the results given in [Di Cecco, Stat.…
We consider estimating the shared mean of a sequence of heavy-tailed random variables taking values in a Banach space. In particular, we revisit and extend a simple truncation-based mean estimator first proposed by Catoni and Giulini. While…
General Central limit theorem deals with weak limits (in type) of sums of row-elements of array random variables. In some situations as in the invariance principle problem, the sums may include only parts of the row-elements. For strictly…
In this paper, we are concerned with the impulsive Duffing equation $$ x''+x^{2n+1}+\sum_{i=0}^{2n}x^{i}p_{i}(t)=0,\ t\neq t_{j}, $$ with impulsive effects $x(t_{j}+)=x(t_{j}-),\ x'(t_{j}+)=-x'(t_{j}-),\ j=\pm1,\pm2,\cdots$, where the time…
We study threshold properties of random constraint satisfaction problems under a probabilistic model due to Molloy. We give a sufficient condition for the existence of a sharp threshold that leads (for boolean constraints) to a necessary…
This paper proves several weak limit theorems for the joint version of extreme order statistics and partial sums of independently and identically distributed random variables. The results are also extended to almost sure limit version.
Tight bounds for several symmetric divergence measures are introduced, given in terms of the total variation distance. Each of these bounds is attained by a pair of 2 or 3-element probability distributions. An application of these bounds…
We present new scalar and matrix Chernoff-style concentration bounds for a broad class of probability distributions over the binary hypercube $\{0,1\}^n$. Motivated by recent tools developed for the study of mixing times of Markov chains on…
Shifted convolution sums play a prominent r\^ole in analytic number theory. We investigate pointwise bounds, mean-square bounds, and average bounds for shifted convolution sums for Hecke eigenforms.
Convergence rate estimates in limit theorems for sums of independent random variables are considered.
We study the sharp bounds of $\mathbb{E}[X_1\cdots X_d]$ when the univariate marginal distributions are known, but the dependence structure between them is unspecified. Maximizing products over non-negative variables is straightforward via…
We revisit the sharp Sobolev inequalities involving boundary terms on Riemannian manifolds with boundaries proved by \emph{[Y.Y. Li and M. Zhu, Geom. Funct. Anal. \textbf{8} (1998), 59--87.]} and explore the role of the mean curvature.
We calculate the p-the moment of the sum of n independent random variables with respect to symmetric norm in R^n. The order of growth for upper bound p/ln p obtained in ths estimate is optimal. The result extends to generalized Lorentz…
This article investigates sharp comparison of moments for various classes of random variables appearing in a geometric context. In the first part of our work we find the optimal constants in the Khintchine inequality for random vectors…
Edgeworth-type expansions for convolutions of probability densities and powers of the characteristic functions with non-uniform error terms are established for i.i.d. random variables with finite (fractional) moments of order $s \geq 2$,…
We investigate finite sections of Gabor frames and study the asymptotic behavior of their lower Riesz bound. From a numerical point of view, these sets of time-frequency shifts are linearly dependent, whereas from a rigorous analytic point…
This paper deals with (finite or infinite) sequences of arbitrary independent events in some probability space. We find sharp lower bounds for the probability of a union of such events when the sum of their probabilities is given. The…