Invariants of Random Knots and Links

Chaim Even-Zohar; Joel Hass; Nati Linial; Tahl Nowik

doi:10.1007/s00454-016-9798-y

Invariants of Random Knots and Links

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

Department of Mathematics

Hebrew University of Jerusalem
University of California at Davis

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

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 language	English
Pages (from-to)	274-314
Number of pages	41
Journal	Discrete and Computational Geometry
Volume	56
Issue number	2
DOIs	https://doi.org/10.1007/s00454-016-9798-y
State	Published - 1 Sep 2016

Bibliographical note

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

Funding

This project was supported by BSF Grant 2012188.

Funders	Funder number
United States-Israel Binational Science Foundation	2012188

Keywords

Finite type invariants
Petaluma
Random knots

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10.1007/s00454-016-9798-y

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AU - Even-Zohar, Chaim

AU - Hass, Joel

AU - Linial, Nati

AU - Nowik, Tahl

PY - 2016/9/1

Y1 - 2016/9/1

N2 - 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.]

AB - 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.]

KW - Finite type invariants

KW - Petaluma

KW - Random knots

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JO - Discrete and Computational Geometry

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ER -

Invariants of Random Knots and Links

Abstract

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Keywords

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