Central limit theorem for linear spectral statistics of block-Wigner-type matrices
arXiv:2110.12171
Abstract
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 via the large-deviation bounds from local law and the cumulant expansion formula. We apply the results to the stochastic block model. Specifically, a class of renormalized adjacency matrices will be block-Wigner-type matrices. Further, we show that for certain estimator of such renormalized adjacency matrices, which will be no longer Wigner-type but share long-range non-decaying weak correlations among the entries, the linear spectral statistics of such estimators will still share the same limiting behavior as those of the block-Wigner-type matrices, thus enabling hypothesis testing about stochastic block model.
arXiv comment5 figures; 53 pages
References in corpus (6)
- Central limit theorem for linear eigenvalue statistics of random matrices with independent entries
- On Asymptotic Properties of Large Random Matrices with Independent Entries
- Gaussian Fluctuation in Random Matrices
- A new method of normal approximation
- Lectures on the local semicircle law for Wigner matrices
- Optimal hypothesis testing for stochastic block models with growing degrees