Invariants of Random Knots and Links

C. Even-Zohar; J. Hass; N. Linial; T. Nowik

doi:10.1007/s00454-016-9798-y

Invariants of Random Knots and Links

C. Even-Zohar, J. Hass, N. Linial, T. Nowik

Technion - Israel Institute of Technology, Bar-Ilan University, The Hebrew University of Jerusalem

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

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	American 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

Keywords

Finite type invariants
Petaluma
Random knots

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1007/s00454-016-9798-y

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AU - Hass, J.

AU - Linial, N.

AU - Nowik, T.

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PY - 2016/9/1

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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

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KW - Random knots

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JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

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ER -

Invariants of Random Knots and Links

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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