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 consider weakly interacting jump processes on time-varying random graphswith dynamically changing multi-color edges. The system consists of a largenumber of nodes in which the node dynamics depends on the joint empiricaldistribution of all the other nodes and the edges connected to it, while theedge dynamics depends only on the corresponding nodes it connects. Asymptoticresults, including law of large numbers, propagation of chaos, and centrallimit theorems, are established. In contrast to the classic McKean-Vlasovlimit, the limiting system exhibits a path-dependent feature in that theevolution of a given particle depends on its own conditional distribution givenits past trajectory. We also analyze the asymptotic behavior of the system whenthe edge dynamics is accelerated. A law of large number and a propagation ofchaos result is established, and the limiting system is given as independentMcKean-Vlasov processes. Error between the two limiting systems, with andwithout acceleration in edge dynamics, is also analyzed.

Mean field interaction on random graphs with dynamically changing multi-color edges