We study random knots and links in R3 using the Petaluma model, which is based on the petal projections developed in . 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 v3. 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. [Figure not available: see fulltext.]
Bibliographical noteFunding Information:
This project was supported by BSF Grant 2012188.
© 2016, Springer Science+Business Media New York.
- Finite type invariants
- Random knots