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