Random Matrix Theory and High Dimensional Statistics

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High dimensional data are becoming increasingly available from a wide range of scientific investigations, including genomics, bioinformatics, engineering, and climate studies. Sound analysis of such datasets poses many statistical challenges. It calls for new statistical theory and methods as well as new technical tools. In this collaborative research project, the investigators will first develop results and technical tools in random matrix theory and then take a unified approach using the technical tools developed to study several important problems in high dimensional statistics as well as applications in signal processing, physics, and mathematics. The statistical and scientific objectives outlined in this proposal are interdisciplinary and will establish connections among different fields - random matrix theory, high dimensional statistics, signal processing, physics, and mathematics. The research will also provide technical tools as well as methodology, to researchers in other scientific fields who collect and analyze high dimensional data. These include, but are not limited to, genomics, biostatistics, and electrical engineering. The procedures and algorithms developed in this project will be implemented and softwares developed will be made freely and publicly available on the web as open sourcecode along with the associated research reports so as to facilitate the dissemination of knowledge.