The <Dirichlet energy space with zero boundary at infinity> is
$$
H_0=\overline{C_c(G)}^{\,\lVert\cdot\rVert_{H_0}},
\qquad
\lVert f\rVert_{H_0}=\mathcal E(f,f)^{1/2},
$$
where $C_c(G)$ is the vector space of finitely supported real functions on the vertices. Transience makes the <Dirichlet form of a Markov chain> positive definite on this completion.

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 226 / 2 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-226/2/a/solution