28 citations · 270 across the 43 of their papers we have counts for
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math.DG2012★ 11 cited
The Expected Total Curvature of Random Polygons
Jason Cantarella, Alexander Y Grosberg, Robert B. Kusner +1
We consider the expected value for the total curvature of a random closed polygon. Numerical experiments have suggested that as the number of edges becomes large, the difference be…
math.DG2012★ 28 cited
Probability Theory of Random Polygons from the Quaternionic Viewpoint
Jason Cantarella, Tetsuo Deguchi, Clayton Shonkwiler
We build a new probability measure on closed space and plane polygons. The key construction is a map, given by Knutson and Hausmann using the Hopf map on quaternions, from the comp…