Asymptotics of the overflow in urn models. (11th September 2022)

• Record Type: Journal Article
• Authors: Gouet, Raul; Hitczenko, Paweł; Wesołowski, Jacek
• Is Part Of: Journal of applied probability. Volume 59:Number 3(2022)
• Page Start: 797
• Page End: 824
• Publication Date: 2022-09-11
• Subjects: Urn model -- occupancy problem -- random allocation -- weak limit theorem; 60F05 -- 60K30 -- 60K35; 519.2
• DOI: 10.1017/jpr.2021.87
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract: Consider a finite or infinite collection of urns, each with capacity r, and balls randomly distributed among them. An overflow is the number of balls that are assigned to urns that already contain r balls. When $r=1$, this is the number of balls landing in non-empty urns, which has been studied in the past. Our aim here is to use martingale methods to study the asymptotics of the overflow in the general situation, i.e. for arbitrary r . In particular, we provide sufficient conditions for both Poissonian and normal asymptotics.