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 are interested in the asymptotics of random trees built by linearpreferential attachment, also known in the literature as Barab\'asi-Alberttrees or plane-oriented recursive trees. We first prove a conjecture of Bubeck,Mossel \& R\'acz concerning the influence of the seed graph on the asymptoticbehavior of such trees. Separately we study the geometric structure of nodes oflarge degrees in a plane version of Barab\'asi-Albert trees via theirassociated looptrees. As the number of nodes grows, we show that theselooptrees, appropriately rescaled, converge in the Gromov-Hausdorff sensetowards a random compact metric space which we call the Brownian looptree. Thelatter is constructed as a quotient space of Aldous' Brownian Continuum RandomTree and is shown to have almost sure Hausdorff dimension $2$.

Scaling limits and influence of the seed graph in preferential attachment trees