Random Band Matrices in the Delocalized Phase, II: Generalized Resolvent Estimates

On Random Matrices Ii

Some Estimates of Norms of Random Matrices

We show that for any random matrix (Xij) with independent mean zero entries E‖(Xij)‖ ≤ C “ max i sX

Spectral Properties of Random Unitary Band Matrices

i It is a pleasure to thank Professor Stoiciu for his patience and selflessness in being my thesis advisor. Second, I would like to thank Professor Silva for being my second reader and for his helpful suggestions. Finally, I would like to thank my parents, without whom I could never have completed this thesis. One of the most important results in analysis is the Spectral Theorem, which shows th...

Analytical Results for Random Band Matrices with

Using the supersymmetry method we analytically calculate the local density of states, the localiztion length, the generalized inverse participation ratios , and the distribution function of eigenvector components for the superpo-sition of a random band matrix with a strongly uctuating diagonal matrix. In this way we extend previously known results for ordinary band matrices to the class of rand...

Perturbations of Diagonal Matrices by Band Random Matrices

We exhibit an explicit formula for the spectral density of a (large) random matrix which is a diagonal matrix whose spectral density converges, perturbated by the addition of a symmetric matrix with Gaussian entries and a given (small) limiting variance profile. 1. Perturbation of the spectral density of a large diagonal matrix In this paper, we consider the spectral measure of a random matrix ...