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

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≥2. 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.