A chain is reversible with respect to $\pi$ when $\pi_iP_{ij}=\pi_jP_{ji}$ for all states. For random walk on a finite connected undirected graph, $\pi_i=\deg(i)/(2|E|)$ satisfies this because both sides equal $1/(2|E|)$ on an edge and zero otherwise.


Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / ib / Paper 1 / 19H / a / Solution

 Solution (source code)