# Stationary distribution (Markov Chains)

Last edited: 2026-02-05

Stationary distribution

For a Markov chain given by $P \in M_{N, N}(\mathbb{R})$, a stationary distribution is a probability distribution given by a vector $\pi \in M_{1,N}(\mathbb{R})$ (this is also a probability matrix ) such that

$$\pi P = \pi.$$