Yau, Horng-TzerYau, Shing-TungJagannath, AukoshChe, Ziliang2019-05-202018-052018-05-112018http://nrs.harvard.edu/urn-3:HUL.InstRepos:40050068This dissertation deals with two random matrix models with dependent entries. The first model is a random matrix with generic slow-varying correlation. The second model is the addition of two Hermitian matrices, conjugated by generic random unitary matrices. For both models, local laws for empirical spectral measures and universality of local spectral statistics are proved.application/pdfenMathematicsThesis or Dissertation2019-05-20