Related papers: Reforming the Wishart characteristic function
We derive an exact formula for the stochastic evolution of the characteristic determinant of a class of deformed Wishart matrices following from a chiral random matrix model of QCD at finite chemical potential. In the WKB approximation, the…
Based on a student research project this article gives a short review on Wishart processes. A Wishart procces is a matrix valued continuous time stochastic process with a marginal Wishart distribution. The Wishart distribution is a matrix…
Using a character expansion method, we calculate exactly the eigenvalue density of random matrices of the form M^\dagger M where M is a complex matrix drawn from a normalized distribution P(M) ~ exp(-\Tr(A M B M^\dagger) with A and B…
We are interested in the distribution of Wishart samples after forgetting their scaling factors. We call such a distribution a projective Wishart distribution. We show that projective Wishart distributions have strong links with the…
A complete characterization of Wishart distributions on the cones of positive semi-definite matrices is provided in terms of a description of their maximal parameter domain. This result is new in that also degenerate scale parameters are…
We establish an explicit expression for the conditional Laplace transform of the integrated Volterra Wishart process in terms of a certain resolvent of the covariance function. The core ingredient is the derivation of the conditional…
We give an approximate formula for the distribution of the largest eigenvalue of real Wishart matrices by the expected Euler characteristic method for the general dimension. The formula is expressed in terms of a definite integral with…
We introduced a generalized Wishart distribution, namely, the Kotz-Wishart distribution. Several existing results based on the normality assumption have been extended. Inspired by the particular form of the pdf of the Kotz-Wishart matrix,…
The Wishart distribution and its generalizations are among the most prominent probability distributions in multivariate statistical analysis, arising naturally in applied research and as a basis for theoretical models. In this paper, we…
Matrix-valued stochastic processes have been of significant importance in areas such as physics, engineering and mathematical finance. One of the first models studied has been the so-called Wishart process, which is described as the…
In this paper, we present a novel test for determining equality in distribution of matrix distributions. Our approach is based on the integral squared difference of the empirical Laplace transforms with respect to the noncentral Wishart…
We study the following question: if $f$ is a nonzero measurable function on $[0,\infty)$ and $m$ and $n$ distinct nonnegative integers, does the ratio $\widehat{f^n}/\widehat{f^m}$ of the Laplace transforms of the powers $f^n$ and $f^m$ of…
The Shilkret integral with respect to a completely maxitive capacity is fully determined by a possibility distribution. In this paper, we introduce a weaker topological form of maxitivity and show that under this assumption the Shilkret…
A characterization of the existence of non-central Wishart distributions (with shape and non-centrality parameter) as well as the existence of solutions to Wishart stochastic differential equations (with initial data and drift parameter) in…
We introduce a one-parameter deformation of the Wishart-Laguerre or chiral ensembles of positive definite random matrices with Dyson index beta=1,2 and 4. Our generalised model has a fat-tailed distribution while preserving the invariance…
These lecture notes provide a comprehensive, self-contained introduction to the analysis of Wishart matrix moments. This study may act as an introduction to some particular aspects of random matrix theory, or as a self-contained exposition…
We analytically derive a decomposition of the lattice fermion determinant for Wilson's Dirac operator with chemical potential into winding sectors, i.e., factors with a fixed number of quarks. Dividing the lattice into four domains, the…
Recently, D. Wang has devised a new contour integral based method to simplify certain matrix integrals. Capitalizing on that approach, we derive a new expression for the probability density function (p.d.f.) of the joint eigenvalues of a…
In this paper we consider the product of a singular Wishart random matrix and a singular normal random vector. A very useful stochastic representation is derived for this product, using which the characteristic function of the product and…
We prove that the number of iterations required to solve a random positive definite linear system with the conjugate gradient algorithm is almost deterministic for large matrices. We treat the case of Wishart matrices $W = XX^*$ where $X$…