Numerical application of knot invariants and universality of random knotting

Tetsuo Deguchi, Kyoichi Tsurusaki
1998 Banach Center Publications  
We study universal properties of random knotting by making an extensive use of isotopy invariants of knots. We define knotting probability (P K (N )) by the probability of an N -noded random polygon being topologically equivalent to a given knot K. The question is the following: for a given model of random polygon how the knotting probability changes with respect to the number N of polygonal nodes? Through numerical simulation we see that the knotting probability can be expressed by a simple
more » ... ction of N . From the result we propose a universal exponent of P K (N ), which may be a new numerical invariant of knots.
doi:10.4064/-42-1-77-85 fatcat:2bop26stobbutn2pkuwjwzsr7q