# 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} }

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…

## References

SHOWING 1-10 OF 36 REFERENCES

### Random Multiplication Approaches Uniform Measure in Finite Groups

- Mathematics
- 2004

In order to study how well a finite group might be generated by repeated random multiplications, P. Diaconis suggested the following urn model. An urn contains some balls labeled by elements which…

### Multiple drawing multi-colour urns by stochastic approximation

- MathematicsJournal of Applied Probability
- 2018

Stochastic approximation methods are applied to multiple drawing Pólya urns, which enables them to prove analogous results to Kuba and Mahmoud, but without the artificial affinity hypothesis, and, for the first time in the literature, in the d-colour case.

### Central limit Theorem for an Adaptive Randomly Reinforced Urn Model

- Mathematics
- 2015

The generalized P\`olya urn (GPU) models and their variants have been investigated in several disciplines. However, typical assumptions made with respect to the GPU do not include urn models with…

### Asymptotic Normality in the Generalized Polya–Eggenberger Urn Model, with an Application to Computer Data Structures

- Mathematics
- 1985

In the generalized Polya–Eggenberger urn model, an urn initially contains a given number of white and black balls. A ball is selected at random from the urn, and the number of white and black balls…

### Convergence of randomized urn models with irreducible and reducible replacement policy

- Mathematics
- 2022

Generalized Friedman urn is one of the simplest and most useful models considered in probability theory. Since Athreya and Ney (1972) showed the almost sure convergence of urn proportions in a…

### Nonlinear randomized urn models: a stochastic approximation viewpoint

- MathematicsElectronic Journal of Probability
- 2019

This paper extends the link between stochastic approximation (SA) theory and randomized urn models developed in Laruelle, Pag{\`e}s (2013), and their applications to clinical trials introduced in…

### Dynamics of an adaptive randomly reinforced urn

- MathematicsBernoulli
- 2018

Adaptive randomly reinforced urn (ARRU) is a two-color urn model where the updating process is defined by a sequence of non-negative random vectors $\{(D_{1,n}, D_{2,n});n\geq1\}$ and randomly…

### Stochastic approximation with random step sizes and urn models with random replacement matrices having finite mean

- Mathematics, Computer ScienceThe Annals of Applied Probability
- 2019

Convergence of the proportion vector, the composition vector and the count vector in $L^1$, and hence in probability is proved.