Finite-Time Behavior of the Annealing Algorithm

In chapter 5 we derived that the probability that an annealing chain has s as its current state will go asymptotically to δ(s, t), the corresponding value of the equilibrium density. Nothing was said however about how fast these probabilities will approach the equilibrium density. Yet it is necessary to know a priori when the actual density is close enough to the equilibrium density to change the value of the control parameter and to start with another chain. In this chapter we want to address that problem.