On the rank of a random symmetric matrix in the large‐deviation regime
Abstract
Abstract Let be an random symmetric matrix with independent identically distributed subgaussian entries of unit variance. We prove the following large‐deviation inequality for the rank of : for all , for some fixed constants . A similar large‐deviation inequality is proven for the rank of the adjacency matrix of dense Erdös–Rényi graphs. This corank estimate enhances the recent breakthrough of Campos, Jensen, Michelen, and Sahasrabudhe that the singularity probability of a random symmetric matrix is exponentially small, and echoes a large‐deviation inequality of Mark Rudelson for the rank of a random matrix with independent entries.
Fields of Study & Subjects
Random Matrices and Applications
Matrix Theory and Algorithms
Publication details
- Journal / source
- Journal of the London Mathematical Society
- Volume
- 113
- Issue
- 6
- Publication date
- 30 May 2026
- Language
- EN