A New Method for Computing the Expected Hitting Time Between Arbitrary Different Configurations of the Multiple–Urn Ehrenfest Model
Year: 2022
Journal of Mathematical Study, Vol. 55 (2022), Iss. 3 : pp. 254–270
Abstract
We study a multiple-urn version of the Ehrenfest model. In this setting, we denote the $n$ urns by Urn $1$ to Urn $n$, where $n\geq2$. Initially, $M$ balls are randomly placed in the $n$ urns. At each subsequent step, a ball is selected and put into the other $n-1$ urns with equal probability. The expected hitting time leading to a change of the $M$ balls' status is computed using the method of stopping times. As a corollary, we obtain the expected hitting time of moving all the $M$ balls from Urn $1$ to Urn $2$.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v55n3.22.03
Journal of Mathematical Study, Vol. 55 (2022), Iss. 3 : pp. 254–270
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Ehrenfest urn model Markov chain random walk hitting time.