given this transition matrix of markov chain
1/2 1/4 1/4 0 1/2 1/2 1 0 0
which represents transition matrix of states a,b,c. a has probability of 1/2 to itself 1/4 to b 1/4 to c. b has probability 1/2 to itself and 1/2 to c c has probability 1 to a.
1) why is state c aperiodic?
I know that it is irreducible and state a is aperiodic because it has self loop so all states are aperiodic. but i can't see why states that don't have self loops are aperiodic.
if one can explain what exactly aperdicity and why state c is aperiodic from the definition of aperiodicity itself.