Invariants of Random Knots and Links

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.

30 pages

References in corpus (3)

• Combinatorial 3-manifolds with 10 vertices
• Knot projections with a single multi-crossing
• Enumeration of closed random walks in the square lattice according to their areas

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• Volumes of Random Alternating Link Diagrams
• Virtual Multicrossings and Petal Diagrams for Virtual Knots and Links
• Petal Projections, Knot Colorings and Determinants
• Random knots in three-dimensional three-colour percolation: numerical results and conjectures
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• Lower Bounds for Electrical Reduction on Surfaces
• Goussarov-Polyak-Viro Conjecture for degree three case
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• Random Colorings in Manifolds
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