Statement
Lemma
For an Ergodic Markov chain with unique stationary distribution
we have
\ \cdots & \pi & \cdots\ \cdots & \pi & \cdots\ \vdots & \vdots & \vdots\ \cdots & \pi & \cdots\ \end{array}\right ).$$
Lemma
For an Ergodic Markov chain with unique stationary distribution
we have
\ \cdots & \pi & \cdots\ \cdots & \pi & \cdots\ \vdots & \vdots & \vdots\ \cdots & \pi & \cdots\ \end{array}\right ).$$