We study universal properties of random knotting by making an extensive use of isotopy invariants of knots. We define knotting probability () 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 , which may be a new numerical invariant of knots.
@article{bwmeta1.element.bwnjournal-article-bcpv42i1p77bwm,
author = {Deguchi, Tetsuo and Tsurusaki, Kyoichi},
title = {Numerical application of knot invariants and universality of random knotting},
journal = {Banach Center Publications},
volume = {43},
year = {1998},
pages = {77-85},
zbl = {0901.57013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv42i1p77bwm}
}
Deguchi, Tetsuo; Tsurusaki, Kyoichi. Numerical application of knot invariants and universality of random knotting. Banach Center Publications, Tome 43 (1998) pp. 77-85. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv42i1p77bwm/
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