Upper bound for intermediate singular values of random matrices

2016/06/13 by Wei, Feng · 1 citation
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1606.03931

openalex publication_date 2016/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove that an n× n matrix A with independent centered subgaussian entries satisfies s_n+1-l(A) ≤ C₁t (l)/(√(n)) with probability at least 1-exp(-C₂tl). This yields s_n-l(A) ∼ (cl)/(√(n)) in combination with a known lower bound. These results can be generalized to the rectangular matrix case.

Cited by

• On the Smallest Singular Value of Log-Concave Random Matrices

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