相关论文: On the fourth moment of a random determinant
In this paper, we determine the sixth moment of the determinant of an asymmetric $n \times n$ random matrix where the entries are drawn independently from an arbitrary distribution $\Omega$ with mean $0$. Furthermore, we derive the…
In this paper, we analyze the second moment of the determinant of random symmetric, Wigner, and Hermitian matrices. Using analytic combinatorics techniques, we determine the second moment of the determinant of Hermitian matrices whose…
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 article we calculate the third and fourth moment of the renormalized intersection local time of a planar Brownian motion. The third moment is calculated anlaytically, the fourth moment numerically. For the closed planar random walk…
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 present an analytic method for computing the moments of a sum of independent and identically distributed random variables. The limiting behavior of these sums is very important to statistical theory, and the moment expressions that we…
This paper deals with sequences of random variables belonging to a fixed chaos of order $q$ generated by a Poisson random measure on a Polish space. The problem is investigated whether convergence of the third and fourth moment of such a…
We prove some inequalities involving fourth central moment of a random variable that takes values in a given finite interval. Both discrete and continuous cases are considered. Bounds for the spread are obtained when a given nxn complex…
We consider the following natural question. Given a matrix $A$ with i.i.d. random entries, what are the moments of the determinant of $A$? In other words, what is $\mathbb{E}[\det(A)^k]$? While there is a general expression for…
We give the first explicit formulas for the joint third and fourth central moments of the multinomial distribution, by differentiating the moment generating function. A general formula for the joint factorial moments was previously given in…
In this brief paper the probability density of a random real, complex and quaternion determinant is rederived using singular values. The behaviour of suitably rescaled random determinants is studied in the limit of infinite order of the…
We prove a version of the multidimensional Fourth Moment Theorem for chaotic random vectors, in the general context of diffusion Markov generators. In addition to the usual componentwise convergence and unlike the infinite-dimensional…
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…
We formulate a version of the Random Wave Conjecture for the fourth moment of Eisenstein series which is based on Zagier's regularized inner product. We prove an asymptotic formula expressing the regularized fourth moment as a mean value of…
Inspired by the insightful article arXiv:1210.7587, we revisit the Nualart-Peccati-criterion arXiv:math/0503598 (now known as the Fourth Moment Theorem) from the point of view of spectral theory of general Markov diffusion generators. We…
We compute the moment of order n of the Poisson stochastic integral of a random process u over a metric space X as a sum that runs over all partitions of {1,...,n} and involves the addition of points to Poisson configurations. This formula…
We present formulas for the (raw and central) moments and absolute moments of the normal distribution. We note that these results are not new, yet many textbooks miss out on at least some of them. Hence, we believe that it is worthwhile to…
We obtain new closed-form formulas for the moments and absolute moments of the variance-gamma distribution. We thus deduce new formulas for the moments and absolute moments of the product of two correlated zero mean normal random variables.
We obtain an asymptotic formula for the fourth moment of central values of a family of quadratic Hecke $L$-functions in the Gaussian field under the generalized Riemann hypothesis (GRH). We also establish lower bounds unconditionally and…
The negative multinomial distribution appears in many areas of applications such as polarimetric image processing and the analysis of longitudinal count data. In previous studies, Mosimann (1963) derived general formulas for the falling…