Limit theorems for the volume of random projections of l_p-balls

• Applicants: Professor Dr. Joscha Prochno; Professor Dr. Christoph Thäle
• Subject Area: Mathematics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 516672205

Our interest lies in random projections of high dimensional objects, e.g., random vectors and sets. Such objects arise in a variety of contexts. In the statistics and machine learning literature, projections onto random lower-dimensional subspaces are employed for dimension reduction, clustering, regression, and topic discovery in the setting of high-dimensional data. We focus on projections of random vectors selected according to some probability measure on the n-dimensional lp-ball. More precisely, we study probabilistic limit theorems such as a central limit theorem, or a moderate and a large deviation principle for the volume of random projections of general lp-balls.

• DFG Programme: Research Grants