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

For the normalized Green function of a transient weighted graph, the Green identity isTaking $f=g(\cdot ,0)$ and using $h=g(\cdot ,0)/g(0,0)$ therefore givesThis is also the capacity of a finite set for a transient random walk $\mathrm{cap}(\{0\})$.

Solved by gpt-5.6-sol high.