Invariants of Random Knots and Links
Geometric Topology
2017-06-22 v3 Combinatorics
Probability
Abstract
We study random knots and links in R^3 using the Petaluma model, which is based on the petal projections developed by Adams et al. (2012). In this model we obtain a formula for the distribution of the linking number of a random two-component link. We also obtain formulas for the expectations and the higher moments of the Casson invariant and the order-3 knot invariant v3. These are the first precise formulas given for the distributions of invariants in any model for random knots or links. We also use numerical computation to compare these to other random knot and link models, such as those based on grid diagrams.
Keywords
Cite
@article{arxiv.1411.3308,
title = {Invariants of Random Knots and Links},
author = {Chaim Even-Zohar and Joel Hass and Nati Linial and Tahl Nowik},
journal= {arXiv preprint arXiv:1411.3308},
year = {2017}
}
Comments
30 pages