Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / ib / Paper 3 / 9H / b / Solution

{title2=$d(i)$}

The period of a state $i$ is the greatest common divisor of its positive-probability return times:
$$
d(i)=\gcd\{n\geq1:P^n(i,i)>0\}.
$$
A state is aperiodic when its period is one.


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