It is shown that certain ensembles of random matrices with entries that vanish outside a band around the diagonal satisfy a localization condition on the resolvent which guarantees that eigenvectors have strong overlap with a vanishing fraction of standard basis vectors, provided the band width W raised to a power μ remains smaller than the matrix size N . For a Gaussian band ensemble, with mat...

We apply local laws of random matrices and free probability theory to study the spectral properties two kernel-based sensor fusion algorithms, nonparametric canonical correlation analysis (NCCA) alternating diffusion (AD), for simultaneously recorded high dimensional datasets under null hypothesis. The matrix interest is product kernel associated with databsets, which may not be diagonalizable ...

We derive a dimension-free Hanson–Wright inequality for quadratic forms of independent sub-gaussian random variables in separable Hilbert space. Our is an infinite-dimensional generalization the classical finite-dimensional Euclidean vectors. illustrate application to generalized $K$-means clustering problem non-Euclidean data. Specifically, we establish exponential rate convergence semidefinit...

The linear vector–valued channel x 7! QiM ix + z with z and M i denoting additive white Gaussian noise and independent random matrices, respectively, is used to model shadowing for BLAST– like communication systems. It is analyzed in the asymptotic regime as the dimensions of the matrices and vectors involved become large by means of free probability theory. It turns out that almost all singula...

2-point topological charge correlation functions of several types of geometric singularity in gaussian random fields are calculated explicitly, using a general scheme: zeros of n-dimensional random vectors, signed by the sign of their jacobian determinant; critical points (gradient zeros) of real scalars in two dimensions signed by the hessian; and umbilic points of real scalars in two dimensio...

y(t) = Ax(t) + e(t) (1) where y(t) ∈ Cm×1 and A = A(θ) ∈ Cm×nθ . It is assumed that: • Emitter signals x(t) are random. • Observation vectors {y(t)}t=1,2,... are i.i.d. circular Gaussian random variables with zero mean (, i.e. eiφZ has the same probability distribution as Z for all real φ, see for example [3]). • The emitter signal x(t) and the noise e(t) are uncorrelated which gives that R(θ, ...

The problem of estimating a random signal vector x observed through a linear transformation H and corrupted by an additive noise is considered. A linear estimator that minimizes the mean squared error (MSE) with a certain selected probability is derived under the assumption that both the additive noise and random signal vectors are zero mean Gaussian with known covariance matrices. Our approach...

In this paper we show that for the purposes of dimensionality reduction certain class of structured random matrices behave similarly to random Gaussian matrices. This class includes several matrices for which matrix-vector multiply can be computed in log-linear time, providing efficient dimensionality reduction of general sets. In particular, we show that using such matrices any set from high d...

We introduce a new class of spatial Cox processes driven by Hilbert-valued random log-intensity. adopt parametric framework in the spectral domain, to estimate its functional correlation structure. Specifically, we consider functional, approach based on periodogram operator, inspired Whittle estimation methodology. Strong consistency estimator is proved linear case. illustrate this property sim...