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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We compute the generating series for the simplest class of bi-free cumulants,beyond free cumulants, the two-bands bi-free cumulants of a pair of a left anda right variable. We also consider two-faced systems with a commutationcondition implying that two-bands moments, that is expectation values of theproduct of a monomial of left and a monomial of right variables determine theother moments. Examples include hyponormal operators, dual systems in freeentropy theory and bi-partite systems.

Free Probability for Pairs of Faces II: 2-Variables Bi-free $R$-Transform and Systems with Rank $\le 1$ Commutation