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Analysis of a class of cannibal urns. (English) Zbl 1245.60029
Summary: We study a class of \(2\times 2\) Polya-Eggenberger urn models, which serves as a stochastic model in biology describing cannibalistic behavior of populations. A special case was studied before by B. Pittel [J. Appl. Probab. 24, 522–526 (1987; Zbl 0637.60017)] using asymptotic approximation techniques, and more recently by H. K. Hwang, the author and A. Panholzer [“Diminishing urn models: analysis of exactly solvable models”, manuscript] using generating functions. We obtain limit laws for the stated class of so-called cannibal urns by using Pittel’s method, and also different techniques.
MSC:
60F05 Central limit and other weak theorems
05C05 Trees
60C05 Combinatorial probability
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