Related papers: Asymptotic *-moments of some random Vandermonde ma…
This work examines various statistical distributions in connection with random Vandermonde matrices and their extension to $d$--dimensional phase distributions. Upper and lower bound asymptotics for the maximum singular value are found to…
Analytical methods for finding moments of random Vandermonde matrices with entries on the unit circle are developed. Vandermonde Matrices play an important role in signal processing and wireless applications such as direction of arrival…
We show that an independent family of uniformly distributed random permutation matrices is asymptotically *-free from an independent family of square complex Gaussian matrices and from an independent family of complex Wishart matrices, and…
We study limit distributions of independent random matrices as well as limit joint distributions of their blocks under normalized partial traces composed with classical expectation. In particular, we are concerned with the ensemble of…
We compute an asymptotic expansion with precision 1/n of the moments of the expected empirical spectral measure of Wigner matrices of size n with independent centered entries. We interpret this expansion as the moments of the addition of…
We consider products of independent large random rectangular matrices with independent entries. The limit distribution of the expected empirical distribution of singular values of such products is computed. The distribution function is…
We study the first and second orders of the asymptotic expansion, as the dimension goes to infinity, of the moments of the Hilbert-Schmidt norm of a uniformly distributed matrix in the p-Schatten unit ball. We consider the case of matrices…
We characterize asymptotic collective behaviour of rectangular random matrices, the sizes of which tend to infinity at different rates: when embedded in a space of larger square matrices, independent rectangular random matrices are…
We study asymptotic distributions of large dimensional random matrices of the form $BB^{*}$, where $B$ is a product of $p$ rectangular random matrices, using free probability and combinatorics of colored labeled noncrossing partitions.…
In this note we study asymptotic properties of the *-distribution of traces of some matrices, with respect to the free Haar trace on the unitary dual group. The considered matrices are powers of the unitary matrix generating the Brown…
This paper studies the asymptotic behaviors of the pairwise angles among n randomly and uniformly distributed unit vectors in R^p as the number of points n -> infinity, while the dimension p is either fixed or growing with n. For both…
Motivated by the recent work on asymptotic independence relations for random matrices with non-commutative entries, we investigate the limit distribution and independence relations for large matrices with identically distributed and Boolean…
We study the asymptotic distribution, as the volume parameter goes to 1, of the peak (largest part) of finite- or slowly-growing-width cylindric plane partitions weighted by their trace, seam, and volume. There are two natural asymptotic…
The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to…
I study the product of independent identically distributed $D\times D$ random probability matrices. Some exact asymptotic results are obtained. I find that both the left and the right products approach exponentially to a probability…
We investigate the universality of singular value and eigenvalue distributions of matrix valued functions of independent random matrices and apply these general results in several examples. In particular we determine the limit distribution…
Geometric properties of $N$ random points distributed independently and uniformly on the unit sphere $\mathbb{S}^{d}\subset\mathbb{R}^{d+1}$ with respect to surface area measure are obtained and several related conjectures are posed. In…
We study Haar unitary random matrices with permuted entries. For a sequence of permutations $\left(\sigma_N\right)_N$, where $\sigma_N$ acts on $N\times N$ matrices we identify conditions under which the $\ast$--distribution of permuted…
Consider large signal-plus-noise data matrices of the form $S + \Sigma^{1/2} X$, where $S$ is a low-rank deterministic signal matrix and the noise covariance matrix $\Sigma$ can be anisotropic. We establish the asymptotic joint distribution…
We study the normalized trace $g_n(z)=n^{-1} \mbox{tr} \, (H-zI)^{-1}$ of the resolvent of $n\times n$ real symmetric matrices $H=\big[(1+\delta_{jk})W_{jk}/\sqrt n\big]_{j,k=1}^n$ assuming that their entries are independent but not…