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Numerical application of knot invariants and universality of random knotting

Tetsuo DeguchiKyoichi 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 function of...

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