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

Many kinds of independence have been defined in non-commutative probabilitytheory. Natural independence is an important class of independence; this classconsists of five independences (tensor, free, Boolean, monotone andanti-monotone ones). In the present paper, a unified treatment of jointcumulants is introduced for natural independence. The way we define jointcumulants enables us not only to find the monotone joint cumulants but also togive a new characterization of joint cumulants for other kinds of naturalindependence, i.e., tensor, free and Boolean independences. We also investigaterelations between generating functions of moments and monotone cumulants. Wefind a natural extension of the Muraki formula, which describes the sum ofmonotone independent random variables, to the multivariate case.

Joint cumulants for natural independence