Random self-avoiding walks on one-dimensional lattices
by
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.