Related papers: On Wishart distribution
We present a generalization of the method of the local relaxation flow to establish the universality of local spectral statistics of a broad class of large random matrices. We show that the local distribution of the eigenvalues coincides…
We study the overlaps between right and left eigenvectors for random matrices of the spherical and truncated unitary ensembles. Conditionally on all eigenvalues, diagonal overlaps are shown to be distributed as a product of independent…
We present an analytic method to determine spectral properties of the covariance matrices constructed of correlated Wishart random matrices. The method gives, in the limit of large matrices, exact analytic relations between the spectral…
The main result of the article is the rate of convergence to the Rosenblatt-type distributions in non-central limit theorems. Specifications of the main theorem are discussed for several scenarios. In particular, special attention is paid…
We examine a generalization of the binomial distribution associated with a strictly increasing sequence of numbers and we prove its Poisson-like limit. Such generalizations might be found in quantum optics with imperfect detection. We…
Recent work has explored data thinning, a generalization of sample splitting that involves decomposing a (possibly matrix-valued) random variable into independent components. In the special case of a $n \times p$ random matrix with…
We consider a versatile matrix model of the form ${\bf A}+i {\bf B}$, where ${\bf A}$ and ${\bf B}$ are real random circulant matrices with independent but, in general, nonidentically distributed Gaussian entries. For this model, we derive…
In the present paper new light is shed on the non-central extensions of the Dirichlet distribution. Due to several probabilistic and inferential properties and to the easiness of parameter interpretation, the Dirichlet distribution proves…
The Poisson distribution has been widely studied and used for modeling univariate count-valued data. Multivariate generalizations of the Poisson distribution that permit dependencies, however, have been far less popular. Yet, real-world…
We show that quaternionic Gaussian random variables satisfy a generalization of the Wick formula for computing the expected value of products in terms of a family of graphical enumeration problems. When applied to the quaternionic Wigner…
We study a well-known problem concerning a random variable $Z$ uniformly distributed between two independent random variables. A new extension has been introduced for this problem and fairly large classes of randomly weighted average…
We consider the statistics of overlaps between a mixed state and its image under random unitary transformations. Choosing the transformations from the unitary group with its invariant (Haar) measure, the distribution of overlaps depends…
Computing and storing probabilities is a hard problem as soon as one has to deal with complex distributions over multiple random variables. The problem of efficient representation of probability distributions is central in term of…
The rate of convergence of the distribution of the length of the longest increasing subsequence, toward the maximal eigenvalue of certain matrix ensembles, is investigated. For finite-alphabet uniform and nonuniform i.i.d. sources, a rate…
We show how the replica method can be used to compute the asymptotic eigenvalue spectrum of a real Wishart product matrix. For unstructured factors, this provides a compact, elementary derivation of a polynomial condition on the Stieltjes…
The technique of wrapping of a univariate probability distribution is very effective in getting a circular form of the underlying density. In this article, we introduce the circular (wrapped) version of xgamma distribution and study its…
We consider the joint distribution of real and imaginary parts of eigenvalues of random matrices with independent real entries with mean zero and unit variance. We prove the convergence of this distribution to the uniform distribution on…
This article derives several properties of the Riesz distributions, such as their corresponding Bartlett decompositions, the inverse Riesz distributions and the distribution of the generalised variance for real normed division algebras. In…
This paper proposes a generalisation of the Pearson type II distribution, which shall termed Pearson Type II-Riesz distribution, based in the Kotz-Riesz distribution. Specifically, the central nonsingular matricvariate generalised Pearson…
We apply the method of determinants to study the distribution of the largest singular values of large $ m \times n $ real rectangular random matrices with independent Cauchy entries. We show that statistical properties of the (rescaled by a…