Related papers: Bulk behaviour of skew-symmetric patterned random …
It is known that the joint limit distribution of independent Wigner matrices satisfies a very special asymptotic independence, called freeness. We study the joint convergence of a few other patterned matrices, providing a framework to…
We study the asymptotic behavior of the spectra of matrices of the form $S_n = \frac{1}{n}XX^*$ where $X =\sum_{r=1}^K X_r$, where $X_r = A_r^\frac{1}{2}Z_rB_r^\frac{1}{2}$, $K \in \mathbb{N}$ and $A_r,B_r$ are sequences of positive…
An equation is obtained for the Stieltjes transform of the normalized distribution of singular values of non-symmetric band random matrices in the limit when the band width and rank of the matrix simultaneously tend to infinity. Conditions…
We study the joint convergence of independent copies of several patterned matrices in the noncommutative probability setup. In particular, joint convergence holds for the well known Wigner, Toeplitz, Hankel, reverse circulant and symmetric…
We show that the spectral radius of an $N\times N$ random symmetric matrix with i.i.d. bounded centered but non-symmetrically distributed entries is bounded from above by $ 2 \*\sigma + o(N^{-6/11+\epsilon}), $ where $\sigma^2 $ is the…
In this paper, we investigate the spectral properties of the sample canonical correlation (SCC) matrix under the alternative hypothesis to provide a more comprehensive description of the association between two sets of variables. Our…
We study two spiked models of random matrices under general frameworks corresponding respectively to additive deformation of random symmetric matrices and multiplicative perturbation of random covariance matrices. In both cases, the…
In Jin et al. (2014), the limiting spectral distribution (LSD) of a symmetrized auto-cross covariance matrix is derived using matrix manipulation, with finite $(2+\delta)$-th moment assumption. Here we give an alternative method using a…
Consider the ensemble of real symmetric Toeplitz matrices, each independent entry an i.i.d. random variable chosen from a fixed probability distribution p of mean 0, variance 1, and finite higher moments. Previous investigations showed that…
Random Matrix Theory (RMT) has successfully modeled diverse systems, from energy levels of heavy nuclei to zeros of $L$-functions; this correspondence has allowed RMT to successfully predict many number theoretic behaviors. However there…
Spectral properties of Hermitian Toeplitz, Hankel, and Toeplitz-plus-Hankel random matrices with independent identically distributed entries are investigated. Combining numerical and analytic arguments it is demonstrated that spectral…
We analyze the spectral distribution of symmetric random matrices with correlated entries. While we assume that the diagonals of these random matrices are stochastically independent, the elements of the diagonals are taken to be correlated.…
We consider a random symmetric matrix ${\bf X} = [X_{jk}]_{j,k=1}^n$ with upper triangular entries being i.i.d. random variables with mean zero and unit variance. We additionally suppose that $\mathbb E |X_{11}|^{4 + \delta} =:…
Real non-symmetric matrices may have either real or complex conjugate eigenvalues. These matrices can be seen to be pseudo-symmetric as $\eta M \eta^{-1} = M^t$, where the metric $\eta$ could be secular (a constant matrix) or depending upon…
A large i.i.d. random matrix with deterministic low-rank perturbation has been extensively studied, particularly in the aspects of the ESD (Empirical Spectral Distribution) and the outliers of eigenvalues. In this work, we investigate the…
Consider the ensembles of real symmetric Toeplitz matrices and real symmetric Hankel matrices whose entries are i.i.d. random variables chosen from a fixed probability distribution p of mean 0, variance 1, and finite higher moments.…
We have calculated the joint probability distribution function for random reverse-cyclic matrices and shown that it is related to an N-body exactly solvable model. We refer to this well-known model potential as a screened harmonic…
We study the spectral norm of large rectangular random Toeplitz and circulant matrices with independent entries. For Toeplitz matrices, we show that the scaled norm converges to the norm of a bilinear operator defined via the pointwise…
We consider ensembles of real symmetric band matrices with entries drawn from an infinite sequence of exchangeable random variables, as far as the symmetry of the matrices permits. In general the entries of the upper triangular parts of…
Szeg\H{o}'s First Limit Theorem provides the limiting statistical distribution (LSD) of the eigenvalues of large Toeplitz matrices. Szeg\H{o}'s Second (or Strong) Limit Theorem for Toeplitz matrices gives a second order correction to the…