Discrete Math Seminar: Harrison Chapman

  • Date: 09/29/2015
  • Time: 16:00
Harrison Chapman, University of Georgia

University of British Columbia


Asymptotic laws for knot diagrams


We consider a model of random knots akin to the one proposed by Dunfield et. al.; a random knot diagram is a random immersion of the circle into the sphere with randomly assigned crossing signs. By studying diagrams as annotated planar maps, we are able to show that any given "tangle diagram" substructure almost certainly occurs many times in a random knot diagram with sufficiently many crossings. Thus, in this model, it is exponentially unlikely for a diagram with n crossings to represent an unknot as n \rightarrow \infty. This asymptotic behavior is similar to that seen in other models of random knots such as random lattice walks and random polygons.

Other Information: 

Location: ESB 4127