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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…
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…
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…
Short cycles of random permutations with cycle weights: point processes approach
Oleksii Galganov, Andrii Ilienko
We study the asymptotic behavior of short cycles of random permutations with cycle weights. More specifically, on a specially constructed metric space whose elements encode all pos…