A New Method for Computing the Expected Hitting Time Between Arbitrary Different Configurations of the Multiple–Urn Ehrenfest Model

A New Method for Computing the Expected Hitting Time Between Arbitrary Different Configurations of the Multiple–Urn Ehrenfest Model

Year:    2022

Author:    Sai Song, Qiang Yao

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 $2$.

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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.

Author Details

Sai Song

Qiang Yao