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

Consider a random walk that has transition matrix:

$P={\begin{bmatrix}1/4&1/4&1/4\\3/4&3/4&1/4\\0&0&1/2\end{bmatrix}}$

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