Restricted random walks on a graph
Statistical Mechanics
2007-05-23 v1 Combinatorics
Abstract
The problem of a restricted random walk on graphs which keeps track of the number of immediate reversal steps is considered by using a transfer matrix formulation. A closed-form expression is obtained for the generating function of the number of n-step walks with r reversal steps for walks on any graph. In the case of graphs of a uniform valence, we show that our result has a probabilistic meaning, and deduce explicit expressions for the generating function in terms of the eigenvalues of the adjacency matrix. Applications to periodic lattices and the complete graph are given.
Cite
@article{arxiv.cond-mat/9812203,
title = {Restricted random walks on a graph},
author = {F. Y. Wu and H. Kunz},
journal= {arXiv preprint arXiv:cond-mat/9812203},
year = {2007}
}
Comments
plain latex, 10 pages, 1 fig., submitted to Ann. Combinatorics