|COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring.|
The Expected Total Curvature of Random Polygons
If you have a question about this talk, please contact Mustapha Amrani.
Topological Dynamics in the Physical and Biological Sciences
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 Cantarella, Deguchi, and Shonkwiler. For this measure, the expected total curvature of a closed n-gon is asymptotic to n pi/2 (2n/2n-3) pi/4. As a consequence, we show that at least 1/3 of fixed-length hexagons and 1/11 of fixed-length heptagons in 3-space are unknotted.
This talk is part of the Isaac Newton Institute Seminar Series series.
This talk is included in these lists:
Note that ex-directory lists are not shown.
Other listsCambridge Network IT & Infrastructure SIG Stokes Society, Pembroke College seminars
Other talksQuantification of near field blast loading Evening Talk: Modern Art and Dance To sense or not to sense viral RNA - essentials of coronavirus innate immune evasion Unveiling the Secrets of High-Performance Datacenters CSaP Annual Conference 2015: How can government make better use of expertise and evidence from the humanities? The Cambridge Cognitive Neuroscience Research Panel