Concentration of Regularized Sparse Random Matrices: Spectral Edge Bounds via Nonbacktracking Operators
正则化稀疏随机矩阵的集中性:基于非回溯算子的谱边界
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 Vershynin (2017), degree regularization enforces concentration at the expected norm scale. However, precise bounds incorporating the cutoffs remain unexplored and challenging since…