|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 listsCalais Migrant Solidarity Trust and Cloud Computing Reproduction on Film: Sex, Secrets and Lies
Other talksThe Ageing Cell Conference 2017 Biomolecular thermodynamics and Calorimetry (ITC) Decadence and the fin de siècle Towards General Artificial Intelligence Diversity of Clathrin Function in Membrane Traffic Design and Evolution of New Biocatalysts for Organic Synthesis