# Character Estimates and Random Walks on *SU(n)*

## Document Type

Presentation Abstract

## Presentation Date

9-27-2010

## Abstract

We say a compact Lie group *G* is *simple* if it is connected, has finite center and is a simple group modulo its center. We study the relationship between character estimates and the structure of conjugacy classes within *G*. Suppose *G* is simple and centerless; the first result shows, for *n* sufficiently large, the set of *n*-fold products from a nontrivial conjugacy class contains the identity as an interior point. This *n* can be chosen uniformly over the set of nontrivial conjugacy classes of *G*. We use this result to prove a uniform estimate on the set of normalized character values of *G*. In an opposite direction, we prove a different type of character estimate, which is used to bound the rate of convergence to Haar measure, for certain conjugation-invariant random walks on *SU*(*n*). This convergence is with respect to the total variation distance of Diaconis and Shashahani.

## Recommended Citation

Manack, Corey, "Character Estimates and Random Walks on *SU(n)*" (2010). *Colloquia of the Department of Mathematical Sciences*. 358.

https://scholarworks.umt.edu/mathcolloquia/358

## Additional Details

Monday, 27 September 2010

3:10 p.m. in Math 103

4:00 p.m. Refreshments in Math Lounge 109