- Reasons:
- 1. The neighborhoods eventually cover the whole space.
- 2. Take any two points .
Suppose ,
**i,j**label states or points in system. - The Metropolis Method is such that probabilities of
transition are , which is and is 1. That is,
- 3. In equilibrium,
- 4. Therefore,
- 5. Here and are number (density) of points
generated at and .

- 1. The neighborhoods eventually cover the whole space.

Geoffrey Fox, Northeast Parallel Architectures Center at Syracuse University, gcf@npac.syr.edu