Peculiar scaling of self-avoiding walk contacts - art. no. 070602

The nearest neighbor contacts between the two halves of an N-site lattice s elf-avoiding walk offer an unusual example of scaling random geometry: for N --> infinity they are strictly finite in number but their radius of gyrat ion R-c is power law distributed proportional to R-c(-tau), where tau > 1 i s a novel exponent characterizing universal behavior. A continuum of diverg ing length scales is associated with the R-c distribution. A possibly super universal tau= 2 is also expected for the contacts of a self-avoiding or ra ndom walk with a confining wall.