Elizabeth S. MeckesCase Western Reserve University
Title: Approximation of projections of random vectors
A classical theorem of Diaconis and Freedman states that, in a limiting sense, "most" projections onto the line of high-dimensional data sets look Gaussian. It is desirable both to quantify this result and to consider higher-dimensional projections, in part in order to investigate how long (i.e., for how large projection dimension) this phenomenon persists. I will discuss an approach to this question which uses many interesting ideas from analysis and probability, including (in no particular order) the concentration of measure phenomenon, Talagrand's generic chaining, p-convexity, entropy, and Stein's method. The talk will not assume prior knowledge of any of these topics.
