Characteristic length of random knotting for cylindrical self-avoiding   polygons
  We discuss the probability of random knotting for a model of self-avoiding polygons whose segments are given by cylinders of unit length with radius $r$. We show numerically that the characteristic length of random knotting is roughly approximated by an exponential function of the chain thickness $r$. 
Miyuki K. shimamura, Tetsuo Deguchi