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Ehrenfest chain. Consider the Ehrenfest chain, Example 1.2, with transition From this we see that…


Ehrenfest chain. Consider the Ehrenfest chain, Example 1.2, with transition

Ehrenfest chain. Consider the Ehrenfest chain, Example 1.2, with transition From this we see that...

From this we see that the mean n converges exponentially rapidly to the equilibrium value of N/2 with the error at time n being (1 – 2/N)n(x – N/2).

Example 1.2

(Ehrenfest Chain). This chain originated in physics as a model for two cubical volumes of air connected by a small hole. In the mathematical version, we have two “urns,” i.e., two of the exalted trash cans of probability theory, in which there are a total of N balls. We pick one of the N balls at random and move it to the other urn.