Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)
Asymptotic laws for knot diagrams
Harrison Chapman  1  
1 : University of Georgia [USA]  -  Website
Athens, GA 30602 -  États-Unis

We study random knotting by considering knot and link diagrams as decorated, (rooted) topological maps on spheres and sampling them with the counting measure on from sets of a fixed number of vertices n. We prove that random rooted knot diagrams are highly composite and hence almost surely knotted (this is the analogue of the Frisch-Wasserman-Delbru ̈ck conjecture) and extend this to unrooted knot diagrams by showing that almost all knot diagrams are asymmetric. The model is similar to one of Dunfield, et al. 

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