Other Statistics and Probability Commons^™

The Expected Total Curvature Of Random Polygons, Jason Cantarella, Alexander Y. Grosberg, Robert Kusner, Clayton Shonkwiler

Robert Kusner

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 between the expected total curvature of a random closed polygon and a random open polygon with the same number of turning angles approaches a positive constant. We show that this is true for a natural class of probability measures on polygons, and give a formula for the constant in terms of the moments of the edgelength distribution.

We then consider the symmetric measure on closed polygons of fixed total length constructed by …