Markov Chains and Potential Theory on Graphs

We briefly review the basic notions of Markovian potential theory in the context of a countable graph equipped with conductances and damping (or killing) rates. These notions include the energy, the Green function, the Dirichlet space, capacitary potentials, the heat semigroup, Fokker–Planck equations, the continuous time Markov chain and Feynman–Kac formula.