Random self-avoiding walks on one-dimensional lattices


Sven Erick Alm and Svante Janson

Uppsala University

In Commun. Statist.-Stochastic Models, 6(2), 169-212 (1990)

For a general class of one-dimensional lattices, we show that the generating function for self-avoiding walks. can be explicitly expressed in terms of a generating matrix. Further, the connective constant can be determined by calculating eigenvalues of the generating matrix. This matrix is also used to get asymptotic results for random self-avoiding walks, in particular a Central Limit Theorem for the endpoint.
The asymptotic results also show that it is possible to define an infinite random self-avoiding walk.
Numerical calculations are performed for strips in the plane square lattice and some other one-dimensional lattices.
The results may be extended to self-avoiding trails and to self-avoiding random walks.

Research supported in part by the Swedish Natural Science Research Council.
1995-02-06, Sven Erick Alm, sea@math.uu.se