Self-avoiding walks with geometrical constraints

We consider self-avoiding walks on aD-dimensional hypercubic lattice, confined to a slab geometry and confined to a half-space. We present a proof of the existence of a connective constant for the slab geometry and review some corresponding results for the half-space. We also discuss the way in which scaling arguments can be used to give stronger, but nonrigorous, results.Presented at the Symposium on Random Walks, Gaithersburg, MD, June 1982.