User-Friendly Tools for Random Matrices: An Introduction
CALIFORNIA INST OF TECH PASADENA DIV OF ENGINEERING AND APPLIED SCIENCE
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Random matrix theory has become a large and vital field of probability, and it has found applications in a wide variety of other areas. To motivate the results in these notes, we begin with an overview of the connections between random matrix theory and computational mathematics. We introduce the basic ideas underlying our approach, and we state one of our main results on the behavior of random matrices. As an application, we examine the properties of the sample covariance estimator, a random matrix that arises in classical statistics. Afterward, we summarize the other types of results that appear in these notes, and we assess the novelties in this presentation.
- Theoretical Mathematics