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 the problem of finding the initial vertex (Adam) in aBarab\'asi--Albert tree process $(\mathcal{T}(n) : n \geq 1)$ at large times.More precisely, given $ \varepsilon>0$, one wants to output a subset $\mathcal{P}_{ \varepsilon}(n)$ of vertices of $ \mathcal{T}(n)$ so that theinitial vertex belongs to $ \mathcal{P}_ \varepsilon(n)$ with probability atleast $1- \varepsilon$ when $n$ is large. It has been shown by Bubeck, Devroye& Lugosi, refined later by Banerjee & Huang, that one needs to output at least$ \varepsilon^{-1 + o(1)}$ and at most $\varepsilon^{-2 + o(1)}$ vertices tosucceed. We prove that the exponent in the lower bound is sharp and the keyidea is that Adam is either a ``large degree" vertex or is a neighbor of a``large degree" vertex (Eve).

Eve, Adam and the Preferential Attachment Tree