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Concentration of Regularized Sparse Random Matrices: Spectral Edge Bounds via Nonbacktracking Operators
In sparse random matrices, spectral outliers (eigenvalues and singular values located away from the bulk) emerge due to degree fluctuations: high degrees inflate the operator norm, while low column degrees reduce the least singular value. As proved by Feige and Ofek (2005) and Le, Levina, and Vershy
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