Establishes full LDPs for the largest eigenvalue of sub-Gaussian Wigner matrices via finite-N approximation by restricted annealed free energies, identifying a transition from GOE rate function to non-universal rate at the onset of eigenvector localization.
Spectral large deviations of sparse random matrices
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Replica-symmetric framework derived for rate functional of empirical spectral distribution fluctuations in diluted Hermitian matrices, with explicit cumulants for Erdős-Rényi adjacency matrices.
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Full large deviation principles for the largest eigenvalue of sub-Gaussian Wigner matrices
Establishes full LDPs for the largest eigenvalue of sub-Gaussian Wigner matrices via finite-N approximation by restricted annealed free energies, identifying a transition from GOE rate function to non-universal rate at the onset of eigenvector localization.
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Replica theory for the rate functional of the empirical spectral distribution function of diluted Hermitian matrices
Replica-symmetric framework derived for rate functional of empirical spectral distribution fluctuations in diluted Hermitian matrices, with explicit cumulants for Erdős-Rényi adjacency matrices.