Spectral distribution of the free unitary Brownian motion: another approach

Details Spectral distribution of the free unitary Brownian motion: another approach Spectral distribution of the free unitary Brownian motion: another approach

2011-03-24

arxiv.org/abs/1103.4693v1

Mathematics

Operator Algebras

Scientific paper

We revisit the description provided by Ph. Biane of the spectral measure of the free unitary Brownian motion. We actually construct for any $t \in (0,4)$ a Jordan curve $\gamma_t$ around the origin, not intersecting the semi-axis $[1,\infty[$ and whose image under some meromorphic function $h_t$ lies in the circle. Our construction is naturally suggested by a residue-type integral representation of the moments and $h_t$ is up to a M\"obius transformation the main ingredient used in the original proof. Once we did, the spectral measure is described as the push-forward of a complex measure under a local diffeomorphism yielding its absolute-continuity and its support. Our approach has the merit to be an easy yet technical exercise from real analysis.

Affiliated with

Also associated with

No associations

Rating

Spectral distribution of the free unitary Brownian motion: another approach 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 Spectral distribution of the free unitary Brownian motion: another approach, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spectral distribution of the free unitary Brownian motion: another approach will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-47186