More precisely, a fundamental result about Markov chains is that a finite state irreducible aperiodic chain has a unique stationary distribution π  and, regardless of the initial state, the time-t distribution of the chain converges to π  as t tends to infinity.
This statement highlights a key property of finite state irreducible aperiodic Markov chains: they have a unique stationary distribution that all future states in the chain will converge to over time. This convergence is independent of the starting point.