RANDOM LINKING OF LATTICE POLYGONS

We study the linking probability of polygons on the simple cubic latti ce. In particular, we consider two polygons each having n edges, confi ned to a cube of side L, and ask for the linking probability as a func tion of n and L. We also consider other situations in which the polygo ns are restricted to be not too far apart, but not necessarily confine d to a cube. We prove several rigorous results, and use Monte Carlo me thods to address some questions which we are unable to answer rigorous ly. An interesting feature is that the linking probability is a functi on of L/n(nu), where nu is the exponent characterizing the radius of g yration of a polygon.