Related papers: Complementary upper bounds for fourth central mome…
We derive some inequalities involving first four central moments of discrete and continuous distributions. Bounds for the eigenvalues and spread of a matrix are obtained when all its eigenvalues are real. Likewise, we discuss bounds for the…
In this paper we shall study noncommutative central moment inequalities with a main focus on whether the commutative bounds are tight in the noncommutative case, or not. We prove that the answer is affirmative for the fourth central moment…
We discuss some extensions and refinements of the variance bounds for both real and complex numbers. The related bounds for the eigenvalues and spread of a matrix are also derived here.
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…
This work is concerned with finite range bounds on the variance of individual eigenvalues of random covariance matrices, both in the bulk and at the edge of the spectrum. In a preceding paper, the author established analogous results for…
The four moment theorem asserts, roughly speaking, that the joint distribution of a small number of eigenvalues of a Wigner random matrix (when measured at the scale of the mean eigenvalue spacing) depends only on the first four moments of…
We obtain variance inequalities for quadratic forms of weakly dependent random variables with bounded fourth moments. We also discuss two application. Namely, we use these inequalities for deriving the limiting spectral distribution of a…
In this paper, we first derive an inequality involving central moments for n real numbers, which in turn provides an extension of Theorem 2.2 of Wolkowicz and Styan [18]. Furthermore, we present refinements of various inequalities obtained…
We study the exact constants in the moment inequalities for sums of centered independent random variables: improve their asymptotics, low and upper bounds, calculate more exact asymptotics, elaborate the numerical algorithm for their…
This paper establishes new upper bounds for the right eigenvalues of monic matrix polynomials over the quaternion division algebra. The noncommutative nature of quaternion multiplication presents fundamental challenges in eigenvalue…
We survey some recent progress on rigorously establishing the universality of various spectral statistics of Wigner random matrix ensembles, focusing in particular on the Four Moment Theorem and its applications.
In this paper, a fourth moment bound for partial sums of functional of strongly ergodic Markov chain is established. This type of inequality plays an important role in the study of empirical process invariance principle. This one is…
Estimates are constructed for the deviation of the concentration functions of sums of independent random variables with finite variances from the folded normal distribution function without any assumptions concerning the existence of the…
In this paper, we generalise the formula for the fourth moment of a random determinant to account for entries with asymmetric distribution. We also derive the second moment of a random Gram determinant.
In order to have a better understanding of finite random matrices with non-Gaussian entries, we study the $1/N$ expansion of local eigenvalue statistics in both the bulk and at the hard edge of the spectrum of random matrices. This gives…
We consider sequences of random variables whose probability generating functions are polynomials all of whose roots lie on the unit circle. The distribution of such random variables has only been sporadically studied in the literature. We…
We obtain optimal moment bounds for Birkhoff sums, and optimal concentration inequalities, for a large class of slowly mixing dynamical systems, including those that admit anomalous diffusion in the form of a stable law or a central limit…
Bounds of the accuracy of the normal approximation to the distribution of a sum of independent random variables are improved under relaxed moment conditions, in particular, under the absence of moments of orders higher than the second.…
We prove quadratic eigenvalue perturbation bounds for generalized Hermitian eigenvalue problems. The bounds are proportional to the square of the norm of the perturbation matrices divided by the gap between the spectrums. Using the results…
We have discussed earlier the correlation functions of the random variables $\det(\la-X)$ in which $X$ is a random matrix. In particular the moments of the distribution of these random variables are universal functions, when measured in the…