Example 11.8 (Ehrenfest Model) The following is a special case of a model, called the Ehrenfest model,3 that has been used to explain diffusion of gases. The general model will be discussed in detail in Section 11.5. We have two urns that, between them, contain four balls. At each step, one of the four balls is chosen at random and moved from the urn that it is in into the other urn. We choose, as states, the number of balls in the rst urn. The transition matrix is then 0 1 2 3 4 0 0 1 0 0 0 1 1/4 0 3/4 0 0 P = 2 0 1/2 0 1/2 0 3 0 0 3/4 0 1/4 4 0 0 0 1 0