Numerical application of knot invariants and universality of random knotting

Tetsuo Deguchi; Kyoichi Tsurusaki

Banach Center Publications (1998)

  • Volume: 42, Issue: 1, page 77-85
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Deguchi, Tetsuo, and Tsurusaki, Kyoichi. "Numerical application of knot invariants and universality of random knotting." Banach Center Publications 42.1 (1998): 77-85. <http://eudml.org/doc/208827>.

@article{Deguchi1998,
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.},
author = {Deguchi, Tetsuo, Tsurusaki, Kyoichi},
journal = {Banach Center Publications},
keywords = {knotting probability},
language = {eng},
number = {1},
pages = {77-85},
title = {Numerical application of knot invariants and universality of random knotting},
url = {http://eudml.org/doc/208827},
volume = {42},
year = {1998},
}

TY - JOUR
AU - Deguchi, Tetsuo
AU - Tsurusaki, Kyoichi
TI - Numerical application of knot invariants and universality of random knotting
JO - Banach Center Publications
PY - 1998
VL - 42
IS - 1
SP - 77
EP - 85
AB - 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.
LA - eng
KW - knotting probability
UR - http://eudml.org/doc/208827
ER -

References

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