standard Gaussian entries. Then \begin{aligned}&\mathbb {E}\sup _{I_0, J_0} \Vert G_A: \ell _p^{J_0} \rightarrow \ell _q^{I_0} \Vert =\mathbb {E}\sup _{I_0, J_0} \sup _{x\in B_p^ {J_0}} \sup _{y\in B_{q^*}^ {I_0}} \sum _{i\in I_0} \sum...
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 ...
A difficult problem in the theory of random tensors is to calculate the expectation values of polynomials in the tensor entries, even in the large N limit and in a Gaussian distribution. Here we address this issue, focusing on a family of polynomials labeled by permutations, which naturally ...
We study the Laguerre and Jacobi versions of this model --- so named by the form of the one-body interaction terms --- and show that for $heta \\\in \\\mathbb Z^+$ they can be realised as the eigenvalue PDF of certain random matrices with Gaussian entries. For general $heta > ...
(5.45) and ∇g−1 is the so-called Jacobian matrix with entries (∇g−1(z))ij≡∂gi−1(z)∂zj. Two-dimensional Gaussian random vectors. For concreteness, we will consider the example of a two-dimensional Gaussian random vector (X1, X2)T with probability density (11.18)p(...
In section 2 we begin by defining a Gaussian random landscape and a Gaussian random supergravity. These landscapes require a detailed understanding of the statistical properties of Gaussian random fields. Therefore, in section 3 we introduce a random matrix description of the various derivatives in ...
9 RegisterLog in Sign up with one click: Facebook Twitter Google Share on Facebook random matrices Collections of large matrices, chosen at random from some ensemble. Random-matrix theory is a branch of mathematics which emerged from the study of complex physical problems, for which a statistica...
Wang, "Stable embedding of Grassmann manifold via Gaussian random matrices," IEEE Transactions on Information Theory, vol. Composite Plate Phased Array Structural Health Monitoring Signal Reconstruction Based on Orthogonal Matching Pursuit Algorithm But in these schemes the encoding matrices are the binary...
We refer to =-=[3]-=- for more discussion of random circulant matrices, and note the result for Gaussian entries is as well given in [3, Corollary 5]. Theorem 1. Suppose X1, X2, . . . are i.i.d. with E(X1) = 0, E(X 2 1 ) ...Meckes, Mark W. (2009). Some results...
Under assumptions on this process, which are satisfied, e.g., by stationary Markov chains on finite sets, by stationary Gibbs measures on finite state spaces, or by Gaussian Markov processes, we show that the limiting spectral distribution depends on the way the matrix is filled with the ...