CMI Silver Jubilee Lecture
Kavita Ramanan, Brown University, U.S.A.
Projections of high-dimensional probability measures
Wednesday, March 11, 2015
Classical theorems in probability theory on i.i.d. (independent and identically distributed) random variables such as the law of large numbers and central limit theorem can be viewed as providing information about certain projections of high-dimensional product measures. Although the study of (typical) projections of more general (non-product) high-dimensional measures dates back to Borel, only recently has a theory begun to emerge, which in particular identifies the role of certain geometric assumptions that lead to better behaved projections. Such questions, besides being of intrinsic interest, are also motivated by applications in statistics and data analysis. We will provide an overview of the classical results, describe recent developments and state some open questions.