[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

In Example, define [math]f(i)[/math] to be the proportion of G genes in state [math]i[/math]. Show that [math]f[/math] is a harmonic function (see Exercise). Why does this show that the probability of being absorbed in state [math](\mbox{GG},\mbox{GG})[/math] is equal to the proportion of G genes in the starting state? (See Exercise.)