Back to Search
Start Over
Asymptotics of the overflow in urn models
- Publication Year :
- 2019
-
Abstract
- Consider a number, finite or not, of urns each with fixed 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 $r=1$, using analytic methods, Hwang and Janson gave conditions under which the overflow (which in this case is just the number of balls landing in non--empty urns) has an asymptotically Poisson distribution as the number of balls grows to infinity. Our aim here is to systematically study the asymptotics of the overflow in general situation, i.~e. for arbitrary $r$. In particular, we provide sufficient conditions for both Poissonian and normal asymptotics for general $r$, thus extending Hwang--Janson's work. Our approach relies on purely probabilistic methods.<br />Comment: 4figures
- Subjects :
- Mathematics - Probability
Primary 60F05, 60K30, secondary 60K35
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1905.06663
- Document Type :
- Working Paper