most recent 30 from http://mathoverflow.net 2013-05-26T00:03:03Z http://mathoverflow.net/feeds/question/88537 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/88537/mixing-time-of-unitary-brownian-motion Marcin Kotowski 2012-02-15T18:43:06Z 2012-02-16T06:24:15Z

<p>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)</p>

http://mathoverflow.net/questions/88537/mixing-time-of-unitary-brownian-motion/88603#88603 Steve Huntsman 2012-02-16T06:24:15Z 2012-02-16T06:24:15Z

<p>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 <a href="http://www.math.cornell.edu/~lsc/hulanrev.pdf" rel="nofollow">this paper</a>.</p>