Mixing time upper bound for the uniformized Rosenthal walk on the special orthogonal groups

Details Mixing time upper bound for the uniformized Rosenthal walk on the special orthogonal groups Mixing time upper bound for the uniformized Rosenthal walk on the special orthogonal groups

2011-10-25

arxiv.org/abs/1110.5394v1

Mathematics

Probability

Scientific paper

We prove that a uniformized variant of both the Rosenthal walk \cite{Rosenthal} and the Kac random walk \cite{Kac} on SO(n) mixes in $\cO(n^3)$ steps in total variation distance. The proof also extends easily to Rosenthal walk with fixed angle $\theta \neq \pi$. To the best of our knowledge, this is the first polynomial time bound for both walks. The techniques employed are mainly from representation theory of SO(n). But a crucial new ingredient is the interpretation of the Fourier coefficients of the character ratio as counting the number of particle cascade paths arising from the classical branching rules.

Affiliated with

Also associated with

No associations

Rating

Mixing time upper bound for the uniformized Rosenthal walk on the special orthogonal groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Mixing time upper bound for the uniformized Rosenthal walk on the special orthogonal groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Mixing time upper bound for the uniformized Rosenthal walk on the special orthogonal groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-93947