# Powers of Random Matrices

Michael Cowling
University of New South Wales, Sydney, Australia
12 September 2011 3-4pm, Carslaw Room 829

## Abstract

If we select an $$n \times n$$ orthogonal matrix $$X$$ "at random", using the uniform distribution on the orthogonal group $$\mathrm{O}(n)$$, then the powers of $$X$$ are not uniformly distributed in $$\mathrm{O}(n)$$. However, as $$n$$ increases, the distribution of $$X^n$$ stabilizes. We prove this, consider generalizations to matrices in other compact Lie groups, and make some remarks about random matrices in other Lie groups.