Related papers: Singular values for products of two coupled random…
The singular values squared of the random matrix product $Y = G_r G_{r-1} \cdots G_1 (G_0 + A)$, where each $G_j$ is a rectangular standard complex Gaussian matrix while $A$ is non-random, are shown to be a determinantal point process with…
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 investigate the hard edge scaling limit of the ensemble defined by the squared singular values of the product of two coupled complex random matrices. When taking the coupling parameter to be dependent on the size of the product matrix,…
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…
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…
Let $X$ be a random matrix whose squared singular value density is a polynomial ensemble. We derive double contour integral formulas for the correlation kernels of the squared singular values of $GX$ and $TX$, where $G$ is a complex Ginibre…
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…
Consider the product of $M$ quadratic random matrices with complex elements and no further symmetry, where all matrix elements of each factor have a Gaussian distribution. This generalises the classical Wishart-Laguerre Gaussian Unitary…
Product matrix processes are multi-level point processes formed by the singular values of random matrix products. In this paper we study such processes where the products of up to $m$ complex random matrices are no longer independent, by…
We study the eigenvalue correlations of random Hermitian $n\times n$ matrices of the form $S=M+\epsilon H$, where $H$ is a GUE matrix, $\epsilon>0$, and $M$ is a positive-definite Hermitian random matrix, independent of $H$, whose…
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…
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…
We find the universal limiting correlation kernels of the Muttalib-Borodin (MB) ensembles with integer parameter $\theta \geq 2$ at $0$ in the transitive regime between the hard edge regime and the soft edge regime. This generalizes the…
We continue investigating spectral properties of a Hermitised random matrix product, which, contrary to previous product ensembles, allows for eigenvalues on the full real line. When a GUE matrix with an external source is involved, we…
We introduce and study a family of random processes with a discrete time related to products of random matrices. Such processes are formed by singular values of random matrix products, and the number of factors in a random matrix product…
Very recently, we have shown how the harmonic analysis approach can be modified to deal with products of general Hermitian and complex random matrices at finite matrix dimension. In the present work, we consider the particular product of a…
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 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…
We compare finite rank perturbations of the following three ensembles of complex rectangular random matrices: First, a generalised Wishart ensemble with one random and two fixed correlation matrices introduced by Borodin and P\'ech\'e,…