Ergodicity

State i is said to be ergodic if it is recurrent, has a period of 1, and has a finite mean recurrence time. If all the states of a Markov chain are ergodic, then it's an ergodic Markov chain. In general terms, a Markov chain is ergodic if there is a number N, such that any state in the system can be reached from any other state in any number of steps greater than or equal to the number N. Therefore, in the case of a fully connected transition matrix, where all transitions have a non-zero probability, this condition is fulfilled with N=1.