Crossing Numbers of Random Two-Bridge Knots

Moshe Cohen; Chaim Even-Zohar; Sunder Ram Krishnan

doi:10.1016/j.topol.2018.08.001

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arXiv · 1606.00277

Crossing Numbers of Random Two-Bridge Knots

Moshe Cohen·Chaim Even-Zohar·Sunder Ram Krishnan

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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.

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BibTeX RIS

Moshe Cohen, Chaim Even-Zohar, Sunder Ram Krishnan. 2016-06-01. Crossing Numbers of Random Two-Bridge Knots. https://doi.org/10.1016/j.topol.2018.08.001

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