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

Let S_{n,k} denote the random geometric graph obtained by placing pointsinside a square of area n according to a Poisson point process of intensity 1and joining each such point to the k=k(n) points of the process nearest to it.  In this paper we show that if Pr(S_{n,k} connected) > n^{-\gamma_1} then theprobability that S_{n,k} contains a pair of `small' components `close' to eachother is o(n^{-c_1}) (in a precise sense of `small' and 'close'), for someabsolute constants \gamma_1>0 and c_1 >0. This answers a question of Walters.(A similar result was independently obtained by Balister.)  As an application of our result, we show that the distribution of theconnected components of S_{n,k} below the connectivity threshold isasymptotically Poisson.

Distribution of components in the k-nearest neighbour random geometric graph for k below the connectivity threshold