A Review of Gaussian Random Matrices

Abstract: While many university students get introduced to the concept of statistics early in their education, random matrix theory (RMT) usually first arises (if at all) in graduate level classes. This thesis serves as a friendly introduction to RMT, which is the study of matrices with entries following some probability distribution. Fundamental results, such as Gaussian and Wishart ensembles, are introduced and a discussion of how their corresponding eigenvalues are distributed is presented. Two well-studied applications, namely neural networks and PCA, are discussed where we present how RMT can be applied