We consider the eigenvalues and eigenvectors of finite, low rank perturbations of random
matrices. Specifically, we prove almost sure convergence of the extreme eigenvalues and …

Random matrix theory is now a big subject with applications in many disciplines of science,
engineering and finance. This article is a survey specifically oriented towards the needs and …

We develop an analytic theory of operator-valued additive free convolution in terms of
subordination functions. In contrast to earlier investigations our functions are not just given …

Covariance analysis of protein sequence alignments uses coevolving pairs of sequence
positions to predict features of protein structure and function. However, current methods …

A bstract We show that in a general\(\mathcal {N}={1}\) supergravity with N≫ 1 scalar fields,
an exponentially small fraction of the de Sitter critical points are metastable vacua. Taking …

The author presents a unified treatment of this highly interdisciplinary topic to help define the
notion of cognitive radio. The book begins with addressing issues such as the fundamental …

We study random graphs with arbitrary distributions of expected degree and derive
expressions for the spectra of their adjacency and modularity matrices. We give a complete …

Abstract Principal Component Analysis (PCA) is a classical method for reducing the
dimensionality of data by projecting them onto a subspace that captures most of their …

In the context of cellular systems, it has been shown that multicell processing can eliminate
inter-cell interference and provide high spectral efficiencies with respect to traditional …

Let S be a positivity‐preserving symmetric linear operator acting on bounded functions. The
nonlinear equation with a parameter z in the complex upper half‐plane ℍ has a unique …