Large dimensional random matrices (LDRM) with specific patterns arise in econometrics,
computer science, mathematics, physics, and statistics. This book provides an easy initiation …

Let $ S= XX^ T $ be the (unscaled) sample covariance matrix where $ X $ is a real $ p\times
n $ matrix with independent entries. It is well known that if the entries of $ X $ are …

Consider random symmetric Toeplitz matrices T_n=(a_ij)_i,j=1^n with matrix entries
a_j,j=0,1,2,⋯, being independent real random variables such that E a_ j= 0,\E| a_ j|^ 2 …

Circulant type matrices have become an important tool in solving differential equations. In
this paper, we consider circulant type matrices, including the circulant and left circulant and …

We present a unified approach to limiting spectral distribution (LSD) of patterned matrices
via the moment method. We demonstrate relatively short proofs for the LSD of common …

In this article, we study the fluctuations of linear statistics of eigenvalues of circulant,
symmetric circulant, reverse circulant, and Hankel matrices. We show that the linear spectral …

We study linear eigenvalue statistics of band Hankel matrices with Brownian motion entries.
We prove that the centred, normalized linear eigenvalue statistics of band Hankel matrices …

Patterned random matrices such as the reverse circulant, the symmetric circulant, the
Toeplitz and the Hankel matrices and their almost sure limiting spectral distribution (LSD) …

Given an ensemble of N× N random matrices, a natural question to ask is whether or not the
empirical spectral measures of typical matrices converge to a limiting spectral measure as …

Abstract Block Toeplitz and Hankel matrices arise in many aspects of applications. In this
paper, we will research the distributions of eigenvalues for some models and get the …