English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We study states on the universal noncommutative *-algebra generated by thecoefficients of a unitary matrix, or equivalently states on the unitary dualgroup. Its structure of dual group in the sense of Voiculescu allows to definefive natural convolutions. We prove that there exists no Haar state for thoseconvolutions. However, we prove that there exists a weaker form of absorbingstate, that we call Haar trace, for the free and the tensor convolutions. Weshow that the free Haar trace is the limit in distribution of the blocks of aHaar unitary matrix when the dimension tends to infinity. Finally, we study aparticular class of free L\'evy processes on the unitary dual group which arealso the limit of the blocks of random matrices on the classical unitary groupwhen the dimension tends to infinity.

Haar states and L\'evy processes on the unitary dual group