Analysis of some exactly solvable diminishing urn models
Abstract
We study several exactly solvable Polya-Eggenberger urn models with a \emph{diminishing} character, namely, balls of a specified color, say are completely drawn after a finite number of draws. The main quantity of interest here is the number of balls left when balls of color are completely removed. We consider several diminishing urns studied previously in the literature such as the pills problem, the cannibal urns and the OK Corral problem, and derive exact and limiting distributions. Our approach is based on solving recurrences via generating functions and partial differential equations.
Keywords
Cite
@article{arxiv.2212.05091,
title = {Analysis of some exactly solvable diminishing urn models},
author = {Hsien-Kuei Hwang and Markus Kuba and Alois Panholzer},
journal= {arXiv preprint arXiv:2212.05091},
year = {2022}
}
Comments
11 pages, 2 figures; appeared in the Proceedings of the Formal Power Series and Algebraic Combinatorics (FPSAC 2007) Nankai University, Tianjin, China, 2007 (only printed proceedings). arXiv admin note: text overlap with arXiv:1110.2425