A random symmetric matrix with i.i.d. subgaussian entries satisfies P(rank at least n-k) at least 1-exp(-c' k n) for k up to c sqrt(n).
Repeated singular values of a random symmetric matrix and decoupled singular value estimates
2 Pith papers cite this work. Polarity classification is still indexing.
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2025 2verdicts
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Establishes quantitative probability bounds on small eigenvalue gaps and singular values for inhomogeneous symmetric subgaussian random matrices, plus improved no-gap delocalization for eigenvectors.
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On the rank of a random symmetric matrix in the large deviation regime
A random symmetric matrix with i.i.d. subgaussian entries satisfies P(rank at least n-k) at least 1-exp(-c' k n) for k up to c sqrt(n).
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The eigenvalue gap of inhomogeneous symmetric discrete random matrix
Establishes quantitative probability bounds on small eigenvalue gaps and singular values for inhomogeneous symmetric subgaussian random matrices, plus improved no-gap delocalization for eigenvectors.