- the irreducibility, the aperiodicity and the reversibility of the Markov chain
- the computation of the acceptance ratio must be possible

Some movements :

birth and death of a free segment

birth and death of a simple connected segment

birth and death of a double connected segment

modifying the orientation of a single or simple connected segment

modifying the length of a single or simple connected segment

modifying the position of a single connected segment

modifying the position of a simple connected segment

Let be *P*_{n} the probability to choose the birth of a free segment
and *P*_{m} the probability to choose to kill one.

The acceptance ratio is :

(22) |

We have :

(23) |

*n*_{d} is the number of free segments in the configuration *S*.

And :

(24) |

We obtain :

(25) |