complex Gaussian entriesIn this paper, we show that complex Gaussian random matrix satisfies the restricted isometric property (RIP) with overwhelming probability. We also show that for compressive sensing (CS) applications, complex Gaussian random matrix outperforms its real number equivalent in the ...
Thorbjornsen, Random matrices with complex Gaussian entries, Exposi- tiones Mathematicae 21 (2003), no. 4, 293-337.Haagerup U., Thorbjorsen S.: Random matrices with complex Gaussian entries. Expositiones Mathematicae 21 (2003), 293-337.
摘要原文 Abstract The probability of small deviations of the determinant of the matrix A A T is estimated, where A is an n ×∞ random matrix with centered entries having the joint Gaussian distribution. The inequality obtained is sharp in a sense. ...
Let $N_{n}$ be a random matrix of order $n$ with entries being i... Friedrich Gtze,A Tikhomirov - 《Annals of Probability》 被引量: 238发表: 2007年 Condition Numbers of Gaussian Random Matrices Let $G_{m imes n}$ be an $m imes n$ real random matrix whose elements are independe...
the eigenvalue probability density function for com- 5plex Hermitian matrices with Gaussian entries is calculated, as is the eigenvalue probability density function for random positive definite matrices MT M with the elements of M complex Gaussians. The characteristic polynomial for both these classes...
Let $N(L)$ be the number of eigenvalues, in an interval of length $L$, of a matrix chosen at random from the Gaussian Orthogonal, Unitary or Symplectic ensembles of ${\\cal N}$ by ${\\cal N}$ matrices, in the limit ${\\cal N}ightarrow\\infty$. We prove that $[N(L) - ...
Let X and Y be two independent L x 1 complex Gaussian random vectors distributed as CN (m×, σ2× IL) and CN (mY, σY2 IL), respectively, where I_L denotes the L x L identity matrix. The joint characteristic function (c.f.) of the real and imaginary parts of the inner produc...
Using the matrices A and B one can fully determine the power spectral density of fluctuations for the Ornstein-Uhlenbeck process. We are interested in the case that the coefficients Aij and Bij are derived from a complex network of interactions with weights drawn at random, possibly with ...
, one is required to put the matrices \({\left\{ {d_k:\textrm{ch}_k \rightarrow \textrm{ch}_{k-1}}\right\} }\) in reduced echelon form, which is a straightforward task in principle. unfortunately, gaussian elimination on an \(m \times m\) matrix incurs an \(o(m^3)\) ...
Symmetry Properties of the k-Body Embedded Unitary Ensemble of Random Matrices We extend the recent study of the k-body embedded Gaussian ensembles by L. Benet, T. Rupp, and H. A. Weidenm眉ller (2001, Benet, Phys. Rev. Lett.87, 101601... Z. Pluha?,HA Weidenmüller - 《Annals of...