Optimal delocalization for generalized Wigner matrices

We study the eigenvectors of generalized Wigner matrices with subexponential entries and prove that they delocalize at optimal rate overwhelming probability. also high probability delocalization bounds sharp constants. Our proof uses an analysis eigenvector moment flow introduced by Bourgade Yau (2017) [18] to bound logarithmic moments for random small Gaussian components. then extend this control all comparison arguments based on a framework regularized eigenvectors, level repulsion, observable employed Landon, Lopatto, Marcinek (2018) [45] compare extremal eigenvalue statistics. Additionally, we repulsion overcrowding estimates entire spectrum, which may be independent interest.