Central Limit Theorem for traces of the resolvents of half-heavy tailed Sample Covariance matrices

2023/07/20 by Svetlana F. Malysheva, Malysheva, Svetlana
Computer Science · Mathematics · #FOS: Mathematics #Matrix Theory and Algorithms #Probability (math.PR) #Random Matrices and Applications #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2307.10848

openalex publication_date 2023/07/20 · openalex created_date 2023/07/22 · openalex updated_date 2026/07/28

Abstract

We consider the spectrum of the Sample Covariance matrix A_N:= (X_N X_N^*)/(N), where X_N is the P× N matrix with i.i.d. half-heavy tailed entries and (P)/(N)→ y>0 (the entries of the matrix have variance, but do not have the fourth moment). We derive the Central Limit Theorem for the Stieltjes transform of the matrix A_N and compute the covariance kernel. Apart from that, we derive the Central Limit Theorem for the Stieltjes transform of overlapping Sample Covariance matrices.

Related

• Central limit theorem for linear spectral statistics of large dimensional separable sample covariance matrices
• Central limit theorem for linear spectral statistics of general separable sample covariance matrices with applications
• Central Limit Theorem for linear eigenvalue statistics of the Wigner and sample covariance random matrices
• Universality of sample covariance matrices: CLT of the smoothed empirical spectral distribution
• A CLT for the LSS of large dimensional sample covariance matrices with unbounded dispersions