On the most expected number of components for random links

2015/07/11 by Ichihara, Kazuhiro, Yoshida, Ken-ichi
#60G50 #FOS: Mathematics #Geometric Topology (math.GT) #Primary 57M25 #Secondary 20F36

paper · doi:10.48550/arxiv.1507.03110

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.

Related

• Random braids and random walks on finite groups
• Linking number of grid models
• Burau representation and random walk on string links
• Volumes of Random Alternating Link Diagrams
• Typical knots: size, link component count, and writhe