Invariants of Random Knots and Links

Chaim Even-Zohar*, Joel Hass, Nati Linial, Tahl Nowik

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


We study random knots and links in R3 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 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.]

Original languageAmerican English
Pages (from-to)274-314
Number of pages41
JournalDiscrete and Computational Geometry
Issue number2
StatePublished - 1 Sep 2016

Bibliographical note

Publisher Copyright:
© 2016, Springer Science+Business Media New York.


  • Finite type invariants
  • Petaluma
  • Random knots


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