Abstract
We obtain a description for the spectral distribution of the free Jacobi process for any initial pair of projections. This result relies on a study of the unitary operator , where are two symmetries and is a free unitary Brownian motion, freely independent from . In particular, for nonnull traces of and , we prove that the spectral measure of possesses two atoms at and an -density on the unit circle for every . Next, via a Szegő-type transformation of this law, we obtain a full description of the spectral distribution of beyond the case where . Finally, we give some specializations for which these measures are explicitly computed.
Citation
Tarek Hamdi. "Spectral distribution of the free Jacobi process, revisited." Anal. PDE 11 (8) 2137 - 2148, 2018. https://doi.org/10.2140/apde.2018.11.2137
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