3 papers
math.PR2026
Explosion and non-explosion in pure birth Crump--Mode--Jagers branching processes
Oleksii Galganov, Andrii Ilienko
In this short note, we provide an explicit sufficient condition for non-explosion of Crump--Mode--Jagers branching processes with pure birth reproduction. It shows that the standar…
math.PR2026
Pareto points in growing dimensions
Andrii Ilienko, Bochen Jin
We consider independent random points uniformly distributed in the -dimensional unit cube and study Pareto points, that is, points that do not coordinatewise dominate any…
math.PR2025
Scaling limit for small blocks in the Chinese restaurant process
Oleksii Galganov, Andrii Ilienko
The Chinese restaurant process is a basic sequential construction of consistent random partitions. We consider random point measures describing the composition of small blocks in s…