Tohoku Mathematical Journal

On the most expected number of components for random links

Kazuhiro Ichihara and Ken-ichi Yoshida

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We consider a random link, which is defined as the closure of a braid obtained from a random walk on the braid group. For such a random link, the expected value for the number of components was calculated by Jiming Ma. In this paper, we determine the most expected number of components for a random link, and further, consider the most expected partition of the number of strings for a random braid.

Article information

Tohoku Math. J. (2), Volume 69, Number 4 (2017), 637-641.

First available in Project Euclid: 2 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 20F36: Braid groups; Artin groups 60G50: Sums of independent random variables; random walks

random link random walk braid


Ichihara, Kazuhiro; Yoshida, Ken-ichi. On the most expected number of components for random links. Tohoku Math. J. (2) 69 (2017), no. 4, 637--641. doi:10.2748/tmj/1512183634.

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