VARIANCE REDUCTION FOR LATTICE WALKS GROWN WITH MARKOV-CHAIN SAMPLING

A Markov chain procedure for growing self- and neighbor-avoiding walks is described. By making the probabilities of all walks nearly equal, the variance in estimates of walk statistics is greatly reduced. A detailed analysis is given of the important example of next-neighbor-avoiding walks on the tetrahedral lattice: Such walks serve as a model for polymethylene chains. This case demonstrates that, in general, a similar variance reduction can be achieved at finite temperature for walks with conformationally dependent internal energy. The algorithm for constructing the sampling distributions for the steps of these finite temperature walks is summarized. © 1979 American Institute of Physics.