Tales of Random Projections

Abstract:

Properties of random projections of high-dimensional probability measures are of interest in a variety of fields, including asymptotic convex geometry, and potential applications to high-dimensional statistics and data analysis.   A particular question of interest is to identify what properties of the high-dimensional measure are captured by its lower-dimensional projections.   While fluctuations of these projections have been well studied over the past decade, we describe more recent work on the tail behavior of such projections, and various implications.  This talk is based on joint works with Nina Gantert, Steven Kim and Yin-Ting Liao.

About the Speaker:

Prof. Ramanan works on probability theory, stochastic processes and their applications. Her focus has been to develop basic mathematical tools for the study of stochastic processes that arise in applications, including those modeling stochastic networks. In recognition of her fundamental work on reflected processes and large deviations, she was awarded the Erlang prize in 2006 for “outstanding contributions to applied probability” by the INFORMS Applied Probability Society.   She is also an elected fellow of the IMS, AMS, INFORMS and AAAS.