This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).
The purpose of this project is threefold: development and analysis of fast, randomized, easily parallelizable algorithms, study of average behavior and limiting distributions for eigenstatistics of large random matrices (which is crucial in understanding the performance of numerical algorithms), and software development for symbolically and numerically computing eigenstatistics of random matrices. To this extent, the investigator will use tools from numerical linear algebra, orthogonal polynomials theory, probability, perturbation theory, and combinatorics.
Numerical linear algebra and stochastic eigenanalysis (classically known as random matrix theory) are mathematical fields with deep and various connections to sciences and engineering, as well as wide and far-reaching applications. One such application is randomized high-performance computing. At a time when an industrial-sized problem is being defined by six or more digits, the astronomical rate of increase in computer processing speed does not compensate for the far slower growth of memory speed; as a result, the processor-memory gap is increasing -- a fact which is now the main obstacle to improved computer performance. Randomization offers a way to successfully address this issue. The project focuses on "transplanting" methods of numerical linear algebra to the study of stochastic eigenanalysis, and using the theoretical results thus obtained for the development of high-performance computational algorithms, as well as in other applications such as the study of Internet networks, building more reliable cell phone networks, and so on. The project also includes several educational endeavors, including initiation of a series of public lectures held at University of Washington to showcase applications of mathematics to sciences, economy, etc. and increasing female participation in undergraduate mathematical competitions.
