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 provide scaling limits for the block counting process and the fixationline of $\Lambda$-coalescents as the initial state $n$ tends to infinity underthe assumption that the measure $\Lambda$ on $[0,1]$ satisfies$\int_{[0,1]}u^{-1}(\Lambda-b\lambda)({\rm d}u)<\infty$ for some $b>0$. Here$\lambda$ denotes the Lebesgue measure. The main result states that the blockcounting process, properly logarithmically scaled, converges in the Skorohodspace to an Ornstein--Uhlenbeck type process as $n$ tends to infinity. Theresult is applied to beta coalescents with parameters $1$ and $b>0$. We splitthe generators into two parts by additively decomposing Lambda and then provethe uniform convergence of both parts separately.

Scaling limits for the block counting process and the fixation line of a class of $\Lambda$-coalescents