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/

Zendy Plus

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

Zendy Tools

Zendy Open

Preferential attachment models form a popular class of growing networks,where incoming vertices are preferably connected to vertices with high degree.We consider a variant of this process, where vertices are equipped with arandom initial fitness representing initial inhomogeneities among vertices andthe fitness influences the attractiveness of a vertex in an additive way. Weconsider a heavy-tailed fitness distribution and show that the model exhibits aphase transition depending on the tail exponent of the fitness distribution. Inthe weak disorder regime, one of the old vertices has maximal degreeirrespective of fitness, while for strong disorder the vertex with maximaldegree has to satisfy the right balance between fitness and age. Our methodsuse martingale methods to show concentration of degree evolutions as well asextreme value theory to control the fitness landscape.

A phase transition for preferential attachment models with additive fitness