Markov Chain Stationary Distribution

A Markov chain with row-stochastic transition matrix $P$ settles into a stationary distribution $\pi$ with $\pi P = \pi$ and $\sum \pi = 1$.

Implement:

• stationary(P): solve the linear system exactly (replace one equation of $(P^\top - I)\pi = 0$ with the normalisation constraint)
• power_iteration(P, iters=1000): start from the uniform distribution and repeatedly apply $\pi \leftarrow \pi P$