# The simple harmonic urn

@article{Crane2011TheSH, title={The simple harmonic urn}, author={Edward Crane and Nicholas Georgiou and Stanislav Volkov and Andrew R. Wade and Robert J. Waters}, journal={Annals of Probability}, year={2011}, volume={39}, pages={2119-2177} }

We study a generalized Polya urn model with two types of ball. If the drawn ball is red, it is replaced together with a black ball, but if the drawn ball is black it is replaced and a red ball is thrown out of the urn. When only black balls remain, the roles of the colors are swapped and the process restarts. We prove that the resulting Markov chain is transient but that if we throw out a ball every time the colors swap, the process is recurrent. We show that the embedded process obtained by… Expand

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