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arXiv · 2409.03921

Expected Natural Density of Countable Sets after Infinitely Iterated de Finetti Lotteries, Computed via Matrix Decomposition

Enciso-Alva·Julio Cesar
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Abstract

Consider a fair lottery over the natural numbers in which the selected number is removed. This lottery is iterated countably infinite times, with a known ratio of iterations to natural numbers. Removed numbers are not replaced. The natural numbers are partitioned into two sets with a given ratio of elements, which is tracked along each iteration of the lottery. Hess and Polisetty considered and investigated such a process and reported the expected values of the densities for some particular cases. In this work, we provide a novel framework for computing these expected densities using infinite matrices. The results presented in this work generalize previous results.

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Enciso-Alva, Julio Cesar. 2024-09-05. Expected Natural Density of Countable Sets after Infinitely Iterated de Finetti Lotteries, Computed via Matrix Decomposition. https://arxiv.org/abs/2409.03921

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