Spectral Radius Concentration Bounds for Inhomogeneous Non-Hermitian Random Matrices
Establishes high-probability upper bounds and concentration inequalities for the spectral radius of square random matrices with independent, mean-zero, non-identically-distributed entries described by a general variance profile S. Results include control by 1+epsilon up to the near-optimal sparsity scale set by the largest entrywise standard deviation, small- and large-deviation inequalities at the spectral edge, and boundedness in heavy-tailed regimes with only 2+epsilon finite moments - all proved by the trace moment method without non-degeneracy or flatness assumptions on S.
SPECTRAL RADIUS CONCENTRATION FOR INHOMOGENEOUS RANDOM MATRICES WITH INDEPENDENT ENTRIES YI HAN
The spectral radius of a matrix is the largest modulus among its eigenvalues; for a non-Hermitian random matrix it is generally far smaller than the operator norm and is governed by genuinely non-Her…