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Random 2-bridge Chebyshev billiard table diagrams
by
Moshe Cohen
Vassar College
Coauthors: Chaim Even-Zohar (Hebrew University of Jerusalem) and Sunder Ram Krishnan (Technion)
Koseleff and Pecker show that all knots can be parametrized by Chebyshev polynomials in three dimensions. These long knots can be realized as trajectories on billiard table diagrams. We use this knot diagram model to study random knot diagrams by flipping a coin at each 4-valent vertex of the trajectory.
We truncate this model to study 2-bridge knots together with the unknot. We give the exact probability of a knot arising in this model. Furthermore, we give the exact probability of obtaining a knot with crossing number c.
Date received: November 17, 2016
Copyright © 2016 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbnq-27.