Gibbs measure (source code)

= Gibbs measure
{c}

A Gibbs measure is a <probability measure> whose finite-block weights or conditional laws are determined by exponential potential sums and their normalization. One must specify whether the convention uses boundary-conditioned finite-volume laws, a normalized one-sided transition kernel, or symbolic Gibbs bounds. For the latter, cylinder probabilities are comparable to $\exp(S_n\phi-nP(\phi))$, where $P$ is <topological pressure>. These conventions have compatibility requirements; an arbitrary unnormalized one-sided potential need not define consistent finite-horizon conditional probabilities.