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 genealogical structure of alleles for aBienaym\'e-Galton-Watson branching process with neutral mutations (infinitealleles model), in the situation where the initial population is large and themutation rate small. We shall establish that for an appropriate regime, theprocess of the sizes of the allelic sub-families converges in distribution to acertain continuous state branching process (i.e. a Jirina process) in discretetime. It\^o's excursion theory and the L\'eevy-It\^o decomposition ofsubordinators provide fundamental insights for the results.

A limit theorem for trees of alleles in branching processes with rare neutral mutations