Circuit processes of order $r$ are defined using a finite class of weighted circuits in a finite set $S$. The probability of the next value of the process is made proportional to the total weight of those circuits in the class which pass through the value in question and the last $r$ values. The process is an order $r$ Markov chain in $S$, and the stationary distribution is easily calculated. Also, it is shown that all stationary order $r$ Markov chains in a finite set can be represented as circuit processes of that order.
"Circuit Processes." Ann. Probab. 9 (4) 604 - 610, August, 1981. https://doi.org/10.1214/aop/1176994365