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August, 1982 Probabilistic Version of a Curvature Formula
Vladimir Drobot
Ann. Probab. 10(3): 860-862 (August, 1982). DOI: 10.1214/aop/1176993798

Abstract

Let $A$ be a $C^2$ curve of length $L(A)$ in some Euclidean space. Let $P_n$ be a sequence of randomly chosen polygons with $n$ vertices which are inscribed in $A$. It is shown that with probability 1 $\lim n^2\lbrack L(A) - L(P_n)\rbrack = \frac{1}{4} \int_A \kappa^2(s) ds$ where $\kappa$ is the curvature.

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Vladimir Drobot. "Probabilistic Version of a Curvature Formula." Ann. Probab. 10 (3) 860 - 862, August, 1982. https://doi.org/10.1214/aop/1176993798

Information

Published: August, 1982
First available in Project Euclid: 19 April 2007

zbMATH: 0486.60016
MathSciNet: MR659557
Digital Object Identifier: 10.1214/aop/1176993798

Subjects:
Primary: 60F15
Secondary: 53A05

Keywords: Random partitions of an internal , Random polygons

Rights: Copyright © 1982 Institute of Mathematical Statistics

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Vol.10 • No. 3 • August, 1982
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