相关论文: Quaternion Gaussian matrices satisfy the RIP
We establish the restricted isometry property for finite dimensional Gabor systems, that is, for families of time--frequency shifts of a randomly chosen window function. We show that the $s$-th order restricted isometry constant of the…
We consider the problem of constructing a linear map from a Hilbert space $\mathcal{H}$ (possibly infinite dimensional) to $\mathbb{R}^m$ that satisfies a restricted isometry property (RIP) on an arbitrary signal model $\mathcal{S} \subset…
We prove that the scaling limits of spin fluctuations in four-dimensional Ising-type models with nearest-neighbor ferromagnetic interaction at or near the critical point are Gaussian. A similar statement is proven for the $\lambda \phi^4$…
We show that quaternionic Gaussian random variables satisfy a generalization of the Wick formula for computing the expected value of products in terms of a family of graphical enumeration problems. When applied to the quaternionic Wigner…
Recently much effort has been made towards the introduction of non-Hermitian random matrix models respecting $PT$-symmetry. Here we show that there is a one-to-one correspondence between complex $PT$-symmetric matrices and split-complex and…
Second order circularity, also called properness, for complex random variables is a well known and studied concept. In the case of quaternion random variables, some extensions have been proposed, leading to applications in quaternion signal…
This paper considers random (non-Hermitian) circulant matrices, and proves several results analogous to recent theorems on non-Hermitian random matrices with independent entries. In particular, the limiting spectral distribution of a random…
In this paper we establish the limit of the empirical spectral distribution of quaternion sample covariance matrices. Suppose $\mathbf X_n = ({x_{jk}^{(n)}})_{p\times n}$ is a quaternion random matrix. For each $n$, the entries…
In this short note we address a gaussian property of normal vectors in random non-Hermitian matrices. The approach uses a simple geometric and comparison technique.
This paper establishes a sharp condition on the restricted isometry property (RIP) for both the sparse signal recovery and low-rank matrix recovery. It is shown that if the measurement matrix $A$ satisfies the RIP condition…
A major enterprise in compressed sensing and sparse approximation is the design and analysis of computationally tractable algorithms for recovering sparse, exact or approximate, solutions of underdetermined linear systems of equations. Many…
In the theory of compressed sensing, restricted isometry analysis has become a standard tool for studying how efficiently a measurement matrix acquires information about sparse and compressible signals. Many recovery algorithms are known to…
It is well known that Gaussian symplectic ensemble (GSE) is defined on the space of $n\times n$ quaternion self-dual Hermitian matrices with Gaussian random elements. There is a huge body of literature regarding this kind of matrices. As a…
In this paper, we derive some necessary and sufficient solvability conditions for some systems of one sided coupled Sylvester-type real quaternion matrix equations in terms of ranks and generalized inverses of matrices. We also give the…
Spectral properties of Gram matrices are central to high dimensional asymptotic analyses of statistical estimators in regression and covariance estimation. These properties, in turn, depend critically on the extreme singular values and…
I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…
We consider four nontrivial ensembles involving Gaussian Wigner and Wishart matrices. These are relevant to problems ranging from multiantenna communication to random supergravity. We derive the matrix probability density, as well as the…
In this brief paper the probability density of a random real, complex and quaternion determinant is rederived using singular values. The behaviour of suitably rescaled random determinants is studied in the limit of infinite order of the…
In this short note, we find an equivalent combinatorial condition only involving finite sums under which a centered Gaussian random vector with multinomial covariance matrix satisfies the Gaussian product inequality (GPI) conjecture. These…
We analyze a multiple-input multiple-output (MIMO) radar model and provide recovery results for a compressed sensing (CS) approach. In MIMO radar different pulses are emitted by several transmitters and the echoes are recorded at several…