Work

On the rank of a random symmetric matrix in the large‐deviation regime

Year: 2026

Type: article

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.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70581

Author: Yi Han

Institution: Massachusetts Institute of Technology

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Simons Foundation

Award: G2363474826