## Discrete Math Seminar: Harrison Chapman

- Date: 09/29/2015
- Time: 16:00

*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.

Location: ESB 4127