Tohoku Mathematical Journal
2017
December
SECOND SERIES VOL. 69, NO. 4

Tohoku Math. J.
69 (2017), 637-641

Title ON THE MOST EXPECTED NUMBER OF COMPONENTS FOR RANDOM LINKS

Author Kazuhiro Ichihara and Ken-ichi Yoshida

(Received September 7, 2015, revised November 27, 2015)
Abstract. 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.

Mathematics Subject Classification. Primary 57M25; Secondary 20F36, 60G50.
Key words and phrases. Random link, random walk, braid.

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