TY - JOUR
T1 - A New Method for Computing the Expected Hitting Time Between Arbitrary Different Configurations of the Multiple–Urn Ehrenfest Model
AU - Song , Sai
AU - Yao , Qiang
JO - Journal of Mathematical Study
VL - 3
SP - 254
EP - 270
PY - 2022
DA - 2022/09
SN - 55
DO - http://doi.org/10.4208/jms.v55n3.22.03
UR - https://global-sci.org/intro/article_detail/jms/20975.html
KW - Ehrenfest urn model, Markov chain, random walk, hitting time.
AB - <p style="text-align: justify;">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&#39; 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 $2$.</p>