In Example 11.11, define f(i) to be the proportion of G genes in state i. Show that

Question:

In Example 11.11, define f(i) to be the proportion of G genes in state i. Show that f is a harmonic function (see Exercise 27). Why does this show that the probability of being absorbed in state (GG,GG) is equal to the proportion of G genes in the starting state? (See Exercise 17.)