Abstract

For large dimensional random band matrices, a famous open question is Anderson’s localization-delocalization transition for the eigenvectors, which states that the eigenvectors of the random band matrix are extended (delocalized) if the band width is larger than the square root of the matrix size, and are otherwise localized. So far, the most hopeful method to attack this question is the supersymmetry method, which is ubiquitous in physics literature. However, the rigorous justification of supersymmetry in mathematics is still notoriously difficult. In this talk, I will introduce a recent result on delocalization of random block band matrices via a rigorous supersymmetry approach.  This is a joint work with Laszlo  Erdos.