The <Dirichlet form of a Markov chain> is
$$
\mathcal E(f,g)=\frac12\sum_{x,y\in S}
\pi(x)P(x,y)(f(x)-f(y))(g(x)-g(y)).
$$
When $P$ is <reversible Markov chain>[reversible], this equals $\langle f,(I-P)g\rangle_\pi$.

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 215 / 3 / a / i / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-215/3/a/i/solution