# 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

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topDeguchi, 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 -

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