• Corpus ID: 254069718

Revisit of a Diaconis urn model

@inproceedings{Yang2022RevisitOA,
  title={Revisit of a Diaconis urn model},
  author={Li Yang and Jiang Hu and Zhidong Bai},
  year={2022}
}

• Li Yang, Jiang Hu, Z. Bai
• Published 29 November 2022
• Mathematics

Let G be a finite Abelian group of order d . We consider an urn in which, initially, there are labeled balls that generate the group G . Choosing two balls from the urn with replacement, observe their labels, and perform a group multiplication on the respective group elements to obtain a group element. Then, we put a ball labeled with that resulting element into the urn. This model was formulated by P. Diaconis while studying a group theoretic algorithm called MeatAxe (Holt and Rees (1994)). Siegmund and Yakir (2004) partially investigated this model. In this paper, we further investigate and generalize this model. More specifically, we allow a random number of balls to be drawn from the urn at each stage in the Diaconis urn model. For such a case, we verify that the normalized urn composition converges almost surely to the uniform distribution on the group G . Moreover, we obtain the asymptotic joint distribution of the urn composition by using the martingale central limit theorem.