@inproceedings{fd99f0f4953f475c909bc7bd143d4d44,

title = "Spectral distribution of the free unitary Brownian motion: Another approach",

abstract = "We revisit the description provided by Ph. Biane of the spectral measure of the free unitary Brownian motion. We actually construct for any τ ∈ (0,4) a Jordan curve γt around the origin, not intersecting the semi-axis [1, ∞] and whose image under some meromorphic function ht 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{\"o}bius 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.",

author = "Nizar Demni and Taoufik Hmidi",

note = "Funding Information: This work was partially supported by Agence Nationale de la recherche grant ANR-09-BLAN-0084-01.",

year = "2012",

doi = "10.1007/978-3-642-27461-9_9",

language = "English (US)",

isbn = "9783642274602",

series = "Lecture Notes in Mathematics",

publisher = "Springer Verlag",

pages = "191--206",

booktitle = "Seminaire de Probabilites XLIV",

}