The Metropolis sampler and simulated annealing
Ehrhard Behrends · Advanced lectures in mathematics · 2000
The setting is as at the beginning of the previous chapter: we are given a finite set $$ \tilde{S} $$ and a function1 $$ H:\tilde{S} \to \mathbb{R} $$ , and this function gives rise to a probability measure $$ {\mathbb{P}_{H}} $$ on $$ \tilde{S} $$ by $$ {\mathbb{P}_{H}}(\{ x\} ): = \frac{{{e^{{ - H(x)}}}}}{z}\quad with\;Z:\sum\limits_{z} {{e^{{ - H(z)}}}} $$ .