Science:Math Exam Resources/Courses/MATH152/April 2012/Question 07 (d)/Statement

Consider a random walk that has transition matrix:

$P=\left[\begin{array}{ccc}1/4& 1/4& 1/4\\ 3/4& 3/4& 1/4\\ 0& 0& 1/2\end{array}\right]$

Based on the results in (b), explain why the probability vector always approaches the equilibrium found in (c), regardless of the initial probability vector $\mathbf{𝐱}(0)$.