## EVENT DETAILS AND ABSTRACT

**Analysis and Probability Seminar**
**Title:** How many typical entries of an orthogonal matrix can be approximated by independent normals?

**Speaker:** Professor Tiefeng Jiang

**Speaker Info:** University of Minnesota

**Brief Description:**

**Special Note**:

**Abstract:**

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

**Time:** 4:10pm

**Where:** Lunt 105

**Contact Person:** Prof. Elton P. Hsu

**Contact email:** elton@math.northwestern.edu

**Contact Phone:** 847-491-8541

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