Related papers: Data Modeling with Large Random Matrices in a Cogn…
We consider a class of real random matrices with dependent entries and show that the limiting empirical spectral distribution is given by the Marchenko-Pastur law. Additionally, we establish a rate of convergence of the expected empirical…
Recent advances in random matrix theory have spurred the adoption of eigenvalue-based detection techniques for cooperative spectrum sensing in cognitive radio. Most of such techniques use the ratio between the largest and the smallest…
Distributed consensus and other linear systems with system stochastic matrices $W_k$ emerge in various settings, like opinion formation in social networks, rendezvous of robots, and distributed inference in sensor networks. The matrices…
Channel properties influence the development of wireless communication systems. Unlike wired channels that are stationary and predictable, radio channels are extremely random and dont offer easy analysis. A Radio Propagation Model (RPM),…
We give an approximate solution to the difficult inverse problem of inferring the topology of an unknown network from given time-dependent signals at the nodes. For example, we measure signals from individual neurons in the brain, and infer…
We study models of weighted exponential random graphs in the large network limit. These models have recently been proposed to model weighted network data arising from a host of applications including socio-econometric data such as migration…
Synchronized measurements of a large power grid enable an unprecedented opportunity to study the spatialtemporal correlations. Statistical analytics for those massive datasets start with high-dimensional data matrices. Uncertainty is…
Missing data occur frequently in a wide range of applications. In this paper, we consider estimation of high-dimensional covariance matrices in the presence of missing observations under a general missing completely at random model in the…
Free probability theory started in the 1980s has attracted much attention lately in signal processing and communications areas due to its applications in large size random matrices. However, it involves with massive mathematical concepts…
In this paper, convergence rates of the spectral distributions of quaternion self-dual Hermitian matrices are investigated. We show that under conditions of finite 6th moments, the expected spectral distribution of a large quaternion…
We briefly review the random matrix theory for large N by N matrices viewed as free random variables in a context of stochastic diffusion. We establish a surprising link between the spectral properties of matrix-valued multiplicative…
Big Data has become the primary source of understanding the structure and dynamics of the society at large scale. The network of social interactions can be considered as a multiplex, where each layer corresponds to one communication channel…
In this paper we derive and analyze two algorithms -- referred to as decentralized power method (DPM) and decentralized Lanczos algorithm (DLA) -- for distributed computation of one (the largest) or multiple eigenvalues of a sample…
The problem of mapping human close-range proximity networks has been tackled using a variety of technical approaches. Wearable electronic devices, in particular, have proven to be particularly successful in a variety of settings relevant…
We describe the distribution of the first finite number of eigenvalues in a newly-forming band of the spectrum of the random Hermitean matrix model. The method is rigorously based on the Riemann-Hilbert analysis of the corresponding…
This paper discusses the need for Cognitive Radio ability in view of the physical scarcity of wireless spectrum for communication. A background of the Cognitive Radio technology is presented and the aspect of 'channel state prediction' is…
In a frequency range where a microwave resonator simulates a chaotic quantum billiard, we have measured moduli and phases of reflection and transmission amplitudes in the regimes of both isolated and of weakly overlapping resonances and for…
In this article, we introduce iterative deterministic equivalents as a novel technique for the performance analysis of communication systems whose channels are modeled by complex combinations of independent random matrices. This technique…
Let $\mathbf X=(X_{jk})$ denote $n\times p$ random matrix with entries $X_{jk}$, which are independent for $1\le j\le n,1\le k\le p$. We consider the rate of convergence of empirical spectral distribution function of the matrix $\mathbf…
We study spectral behavior of sparsely connected random networks under the random matrix framework. Sub-networks without any connection among them form a network having perfect community structure. As connections among the sub-networks are…