Percolation of Linked Circles

  • Y. Diao
  • E. J. Janse van Rensburg
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 103)

Abstract

Let P δ be a Poission process with density,δ in R.3, and let each point in the Poisson process be the center of a unit circle with normal vector a uniform random variable on the 2-sphere. Is there a critical density of the Poisson process such that there exists an infinite unsplittable link of circles? Clearly, if δ=0, then no such infinite unsplittable link exists, and if δ approaches ∞, then it becomes likely that an infinite unsplittable link exists. We prove that there exists an infinite unsplittable link at a finite value of δ. Similar results are true for other models of random closed curves that do not have the volume exclusion property.

Keywords

Knots Links Knotted Polygons Percolation. 

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Copyright information

© Springer-Verlag New York, Inc. 1998

Authors and Affiliations

  • Y. Diao
    • 1
  • E. J. Janse van Rensburg
    • 2
  1. 1.Department of MathematicsUniversity of North Carolina at CharlotteCharlotteUSA
  2. 2.Department of Mathematics and StatisticsYork University, North YorkOntarioCanada

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