It is instructive to calculate some probabilities occurring in the RIS model. An important probability for computer simulations is the conditional probability defined below. We shall always assume that the chain is infinitely long, and that end effects may be neglected. In this case is the only eigenvalue we need.

We define the probability that a given bond is in state
by

(1.19) |

Explicitly introducing the averaging procedure yields

(1.20) |

Using the same method as in the previous section we find

= | |||

= | |||

= | (1.21) |

Dividing numerator and denominator by , and assuming

(1.22) |

Because here and in the remaining part of the chapter we only need and the corresponding vectors

Similarly one calculates

An important quantity is , the conditional probability to find bond

(1.25) |

Introducing Eqs. (1.23) and (1.24) we get

(1.26) |

This quantity may be used to generate chain conformations on a computer.