Crossing Numbers of Random Two-Bridge Knots
Geometric Topology
2018-08-13 v1 Combinatorics
Probability
Abstract
In a previous work, the first and third authors studied a random knot model for all two-bridge knots using billiard table diagrams. Here we present a closed formula for the distribution of the crossing numbers of such random knots. We also show that the probability of any given knot appearing in this model decays to zero at an exponential rate as the length of the billiard table goes to infinity. This confirms a conjecture from the previous work.
Keywords
Cite
@article{arxiv.1606.00277,
title = {Crossing Numbers of Random Two-Bridge Knots},
author = {Moshe Cohen and Chaim Even-Zohar and Sunder Ram Krishnan},
journal= {arXiv preprint arXiv:1606.00277},
year = {2018}
}