Article ID Journal Published Year Pages File Type
4658165 Topology and its Applications 2015 18 Pages PDF
Abstract

We use the Chebyshev knot diagram model of Koseleff and Pecker in order to introduce a random knot diagram model by assigning the crossings to be positive or negative uniformly at random. We give a formula for the probability of choosing a knot at random among all knots with bridge index at most 2. Restricted to this class, we define internal and external reduction moves that decrease the number of crossings of the diagram. We make calculations based on our formula, showing the numerics in graphs and providing evidence for our conjecture that the probability of any knot appearing in this model decays to zero as the number of crossings goes to infinity.

Related Topics
Physical Sciences and Engineering Mathematics Geometry and Topology
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