2008/08/19 by Sourav Chatterjee, Michel Ledoux, Chatterjee, Sourav +1
Mathematics · #15A52 #60E15 #Advanced Combinatorial Mathematics #FOS: Mathematics #Graph theory and applications #Probability (math.PR) #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.0808.2521
openalex publication_date 2008/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let M be an arbitrary Hermitian matrix of order n, and k be a positive integer less than or equal to n. We show that if k is large, the distribution of eigenvalues on the real line is almost the same for almost all principal submatrices of M of order k. The proof uses results about random walks on symmetric groups and concentration of measure. In a similar way, we also show that almost all k x n submatrices of M have almost the same distribution of singular values.