Related papers: Two-sided inequalities for the density function's …
The generalized Marcum functions $Q_{\mu}(x,y)$ and $P_{\mu}(x,y)$ have as particular cases the non-central $\chi^2$ and gamma cumulative distributions, which become central distributions (incomplete gamma function ratios) when the…
A classical statistical inequality is used to show that the distance covariance of two bounded random vectors is bounded from above by a simple function of the dimensionality and the bounds of the random vectors. Two special cases that…
We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in…
A new lower boundary for the product of variances of two observables is obtained in the case, when these observables are entangled with the third one. This boundary can be higher than the Robertson--Schr\"odinger one. The special case of…
We study the dynamics of upper and lower bounds of squared concurrence.Our results are similar to that of Konard et al. and can help the estimation of high-dimension bipartite entanglement in experiments.
A central limit theorem for the integrated squared error of the directional-linear kernel density estimator is established. The result enables the construction and analysis of two testing procedures based on squared loss: a nonparametric…
We study two-faced families of random variables having bi-free infinitely divisible distributions. We prove a limit theorem of the sums of bi-free two-faced pairs of random variables within a triangular array. Then, by using the full Fock…
Gaussian random fields on Euclidean spaces whose variances reach their maximum values at unique points are considered. Exact asymptotic behaviors of probabilities of large absolute maximum of theirs trajectories have been evaluated using…
We propose a random bipartite graph with weights assigned to both parts of the vertex sets. Edges are formed independently with probabilities that depend on these weights. This bipartite graph naturally gives rise to a random intersection…
We describe various aspects of two-dimensional $N=2$ supergravity in superspace. We present the solution to the constraints in terms of unconstrained prepotentials, and the different superspace measures (full and chiral) used in the…
For linear models with spatial errors, the empirical likelihood ratio statistics are constructed for the parameters of the models. It is shown that the limiting distributions of the empirical likelihood ratio statistics are chi-squared…
We point out that double distributions need not vanish at their boundary. Boundary terms do not change the ambiguity inherent in defining double distributions; instead, boundary conditions must be satisfied in order to switch between…
We study the fully entangled fraction of quantum states. An upper bound is obtained for arbitrary dimensional bipartite systems. This bound is shown to be exact for the case of two-qubit systems. An inequality related the fully entangled…
We establish Strichartz estimates (both reversed and some direct ones), pointwise decay estimates, and weighted decay estimates for the linear wave equation in dimension two with an almost scaling-critical potential, in the case when there…
We prove two-sided inequalities between the integral moduli of smoothness of a function on $\mathbb{R}^d/\mathbb{T}^d$ and the weighted tail-type integrals of its Fourier transform/series. Sharpness of obtained results in particular is…
Consider a measure $\mu_\lambda = \sum_x \xi_x \delta_x$ where the sum is over points $x$ of a Poisson point process of intensity $\lambda$ on a bounded region in $d$-space, and $\xi_x$ is a functional determined by the Poisson points near…
New positivity bounds are derived for generalized (off-forward) parton distributions using the impact parameter representation. These inequalities are stable under the evolution to higher normalization points. The full set of inequalities…
In this paper, we improve the moment estimates for the gaps between numbers that can be represented as a sum of two squares of integers. We consider certain sum of Bessel functions and prove the upper bound for its weighted mean value. This…
Chebyshev's inequality provides an upper bound on the tail probability of a random variable based on its mean and variance. While tight, the inequality has been criticized for only being attained by pathological distributions that abuse the…
We give a general local central limit theorem for the sum of two independent random variables, one of which satisfies a central limit theorem while the other satisfies a local central limit theorem with the same order variance. We apply…