Related papers: Singular value correlation functions for products …
We discuss the product of $M$ rectangular random matrices with independent Gaussian entries, which have several applications including wireless telecommunication and econophysics. For complex matrices an explicit expression for the joint…
The product of M complex random Gaussian matrices of size N has recently been studied by Akemann, Kieburg and Wei. They showed that, for fixed M and N, the joint probability distribution for the squared singular values of the product matrix…
The squared singular values of the product of $M$ complex Ginibre matrices form a biorthogonal ensemble, and thus their distribution is fully determined by a correlation kernel. The kernel permits a hard edge scaling to a form specified in…
Akemann, Ipsen and Kieburg recently showed that the squared singular values of products of M rectangular random matrices with independent complex Gaussian entries are distributed according to a determinantal point process with a correlation…
We study the singular values of the product of two coupled rectangular random matrices as a determinantal point process. Each of the two factors is given by a parameter dependent linear combination of two independent, complex Gaussian…
We consider the product of n complex non-Hermitian, independent random matrices, each of size NxN with independent identically distributed Gaussian entries (Ginibre matrices). The joint probability distribution of the complex eigenvalues of…
We consider the singular value statistics of products of independent random matrices. In particular we compute the corresponding averages of products of characteristic polynomials. To this aim we apply the projection formula recently…
It has been shown by Akemann, Ipsen and Kieburg that the squared singular values of products of $M$ rectangular random matrices with independent complex Gaussian entries are distributed according to a determinantal point process with a…
Akemann, Ipsen, and Kieburg showed recently that the squared singular values of a product of M complex Ginibre matrices are distributed according to a determinantal point process. We introduce the notion of a polynomial ensemble and show…
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…
Complex Hermitian random matrices with a unitary symmetry can be distinguished by a weight function. When this is even, it is a known result that the distribution of the singular values can be decomposed as the superposition of two…
The eigenvalue statistics for complex $N \times N$ Wishart matrices $X_{r,s}^\dagger X_{r,s}$, where $ X_{r,s}$ is equal to the product of $r$ complex Gaussian matrices, and the inverse of $s$ complex Gaussian matrices, are considered. In…
Let $\mathbf{H}=(h_{ij})$ and $\mathbf{G}=(g_{ij})$ be two $m\times n$, $m\leq n$, random matrices, each with i.i.d complex zero-mean unit-variance Gaussian entries, with correlation between any two elements given by…
We study the singular values of certain triangular random matrices. When their elements are i.i.d. standard complex Gaussian random variables, the squares of the singular values form a biorthogonal ensemble, and with an appropriate change…
We calculate the `one-point function', meaning the marginal probability density function for any single eigenvalue, of real and complex Wishart correlation matrices. No explicit expression had been obtained for the real case so far. We…
The singular values of products of standard complex Gaussian random matrices, or sub-blocks of Haar distributed unitary matrices, have the property that their probability distribution has an explicit, structured form referred to as a…
We consider a class of sample covariance matrices of the form $Q=TXX^{*}T^*,$ where $X=(x_{ij})$ is an $M \times N$ rectangular matrix consisting of i.i.d entries and $T$ is a deterministic matrix satisfying $T^*T$ is diagonal. Assuming $M$…
We prove that the squared singular values of a fixed matrix multiplied with a truncation of a Haar distributed unitary matrix are distributed by a polynomial ensemble. This result is applied to a multiplication of a truncated unitary matrix…
In this study, we derive the exact distributions of eigenvalues of a singular Wishart matrix under an elliptical model. We define generalized heterogeneous hypergeometric functions with two matrix arguments and provide convergence…
We consider a product of an arbitrary number of independent rectangular Gaussian random matrices. We derive the mean densities of its eigenvalues and singular values in the thermodynamic limit, eventually verified numerically. These…