In applied multivariate statistics, estimating the number of latent dimensions or the number of
clusters is a fundamental and recurring problem. One common diagnostic is the scree plot …

We consider the spectral properties of balanced stochastic block models of which the
average degree grows slower than the number of nodes (sparse regime) or proportional to it …

Motivated by the stochastic block model, we investigate a class of Wigner-type matrices with
certain block structures and establish a CLT for the corresponding linear spectral statistics …

A Laplacian matrix is a real symmetric matrix whose row and column sums are zero. We
investigate the limiting distribution of the largest eigenvalue of a Laplacian random matrix …

We show that the fluctuations of the largest eigenvalue of any generalized Wigner matrix H
converge to the Tracy–Widom laws at a rate nearly O (N− 1∕ 3), as the matrix dimension N …

Often in the study of eigenvalues of random matrices, one considers matrices whose entries
are independent random variables, possibly up to some symmetry condition on the matrix …

This work is devoted to the estimation of the convergence rate of the empirical spectral
distribution function (ESD) of sparse sample covariance matrices in the Kolmogorov metric …

Networks are one of the basic structures to represent the relations between objects. There is
a lot of application of random networks in daily life, including social networks, evolution …

We consider the eigenvalues of a fixed, non-normal matrix subject to a small additive
perturbation. In particular, we consider the case when the fixed matrix is a banded Toeplitz …

We consider sparse sample covariance matrices with sparsity probability with. Assuming
that the distribution of matrix elements has a finite absolute moment of order,, it is shown that …