Title: How many typical entries of an orthogonal matrix can be approximated by independent normals?
Speaker: Professor Tiefeng Jiang
Speaker Info: University of Minnesota
I will present my solution to the well-known open problem by Diaconis stated as follows: what are the largest order of p and q such that Z, the p by q left upper block of an n by n typical orthogonal matrix T, can be approximated by independent normals? This problem is solved by two different approximation methods. First, we show that the largest orders of p and q are the square root of n in the sense of approximation by the variation norm. Second, look at the elements of the first m columns of a typical orthogonal matrix, generated by performing the Gram-Schmidt procedure on a square matrix with independent standard normals as entries. We show that the largest order of m, such that a weak distance between the two m columns of elements in both matrices goes to zero in probability, is n/log(n). A history from 1906 to 2003 of the problem from Mechanics, Statistics and Imagine Analysis will also be presented.Date: Monday, November 15, 2004