Summary: The authors study universal properties of random knotting by making an extensive use of isotopy invariants of knots. They 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 the authors see that the knotting probability can be expressed by a simple function of \(N\). From the result they propose a universal exponent of \(P_K(N)\), which may be a new numerical invariant of knots.
For the entire collection see [Zbl 0890.00048].