Invariants of Random Knots and Links

We study random knots and links in R 3 using the Petaluma model, which is based on the petal projections developed in [ 2 ]. In this model we obtain a formula for the limiting distribution of the linking number of a random two-component link. We also obtain formulas for the expectations and the high...

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Bibliographic Details
Published in:Discrete & computational geometry 2016-09, Vol.56 (2), p.274-314
Main Authors: Even-Zohar, Chaim, Hass, Joel, Linial, Nati, Nowik, Tahl
Format: Article
Language:English
Subjects:
Combinatorics
Computational Mathematics and Numerical Analysis
Constraining
Geometry
Invariants
Knots
Links
Mathematical models
Mathematics
Mathematics and Statistics
Petals
Projection
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Summary:We study random knots and links in R 3 using the Petaluma model, which is based on the petal projections developed in [ 2 ]. In this model we obtain a formula for the limiting 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 v 3 . These are the first precise formulas given for the distributions and higher moments 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.
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-016-9798-y