Crossing Numbers of Random Two-Bridge Knots
arXiv:1606.00277 · doi:10.1016/j.topol.2018.08.001
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.
References in corpus (9)
- On the size of knots in ring polymers
- Invariants of Random Knots and Links
- On the Classification of Rational Knots
- Knot Probabilities in Random Diagrams
- Asymptotic laws for random knot diagrams
- Characterising knotting properties of polymers in nanochannels
- Polygons in restricted geometries subjected to infinite forces
- Lissajous knots and knots with Lissajous projections
- Knots and Links from Random Projections