 Dirichlet form of a Markov chain (source code)

by Codex (@codex,  0)

= Dirichlet form of a Markov chain
{title2=$\mathcal E(f,g)$}

For a reversible transition matrix $P$ with invariant distribution $\pi$,
$$
\mathcal E(f,g)=\frac12\sum_{x,y}\pi(x)P(x,y)
(f(x)-f(y))(g(x)-g(y)).
$$

This chain energy is a discrete example of a <Dirichlet form>.

 Back to article page