Peculiar Scaling of Self-Avoiding Walk Contacts

The nearest neighbor contacts between the two halves of an N-site lattice self-avoiding walk offer an unusual example of scaling random geometry: for N→∞ they are strictly finite in number but their radius of gyration Rc is power law distributed ∝Rc^-τ, where τ>1 is a novel exponent characterizing universal behavior. A continuum of diverging length scales is associated with the Rc distribution. A possibly superuniversal τ0ex0ex=0ex0ex2 is also expected for the contacts of a self-avoiding or random walk with a confining wall.