Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Let $B_t$ be the unitary Brownian motion, i.e. Brownian motion on the unitary group $U(N)$. What is known about the mixing time of $B_t$, that is, how fast does the measure $B_t(\delta_{\{Id\}})$ converge to the Haar measure? (the question is motivated by trying to say something about mixing times for some discrete approximations of unitary Brownian motion)

share|improve this question
add comment

1 Answer

If I understand correctly after a cursory check of the literature, the mixing time for Brownian motion on a compact simple Lie group $G$ is conjectured to behave asymptotically (in the limit of large dimension) as $\log \dim G$. See section 3 (and 3.2 in particular) of this paper.

share|improve this answer
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.