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Numerical application of knot invariants and universality of random knotting

Volume 42 / 1998

Banach Center Publications 42 (1998), 77-85 DOI: 10.4064/-42-1-77-85

Abstract

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 N. From the result we propose a universal exponent of $P_K(N)$, which may be a new numerical invariant of knots.

Authors

• Tetsuo Deguchi
• Kyoichi Tsurusaki

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