# Today I Learned

Some of the things I've learned every day since Oct 10, 2016

## 52: Ergodicity in Markov Chains

A state $s$ in a Markov chain $X$ is ergodic iff it is aperiodic and recurrent. If all states in a Markov chain are ergodic, then the chain itself is said to be ergodic. This is equivalent to the condition that there is a number $n$ such that any state in $X$ can be reached by any other state in exactly $n$ steps.