RANDOM LINKING OF LATTICE POLYGONS

We study the linking probability of polygons on the simple cubic lattice. In particular, we consider two polygons each having n edges, confined to a cube of side L, and ask for the linking probability as a function of n and L. We also consider other situations in which the polygons are restricted to be not too far apart, but not necessarily confined to a cube. We prove several rigorous results, and use Monte Carlo methods to address some questions which we are unable to answer rigorously. An interesting feature is that the linking probability is a function of L/n(nu), where nu is the exponent characterizing the radius of gyration of a polygon.