Restricted random walks on a graph

Details Restricted random walks on a graph Restricted random walks on a graph

1998-12-11

arxiv.org/abs/cond-mat/9812203v1

Ann. Combinatorics 3, 475-481 (1999)

Physics

Condensed Matter

Statistical Mechanics

plain latex, 10 pages, 1 fig., submitted to Ann. Combinatorics

Scientific paper

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.

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