Brownian motion is a continuum scaling limit for a wide class of random processes, and
there has been great success in develo** a theory for its properties (such as distribution …

Cognitive radio is widely expected to be the next Big Bang in wireless communications.
Spectrum sensing, that is, detecting the presence of the primary users in a licensed …

The idea for this book came from the time the authors spent at the Statistics and Applied
Mathematical Sciences Institute (SAMSI) in Research Triangle Park in North Carolina …

Random quantum circuits yield minimally structured models for chaotic quantum dynamics,
which are able to capture, for example, universal properties of entanglement growth. We …

The aim of this book is to investigate the spectral properties of random matrices (RM) when
their dimensions tend to infinity. All classical limiting theorems in statistics are under the …

The theory of random matrices plays an important role in many areas of pure mathematics
and employs a variety of sophisticated mathematical tools (analytical, probabilistic and …

Let x (1) denote the square of the largest singular value of an n× p matrix X, all of whose
entries are independent standard Gaussian variates. Equivalently, x (1) is the largest …

Spectrum sensing is a fundamental component in a cognitive radio. In this paper, we
propose new sensing methods based on the eigenvalues of the covariance matrix of signals …

The authors consider the length, $ l_N $, of the longest increasing subsequence of a
random permutation of $ N $ numbers. The main result in this paper is a proof that the …

We compute the limiting distributions of the largest eigenvalue of a complex Gaussian
sample covariance matrix when both the number of samples and the number of variables in …