# 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.
1995-02-06, Sven Erick Alm, sea@math.uu.se