Efron's Mean Volume Formula in Higher Dimensions
Dominik Beck
TL;DR
This paper extends Efron's classical result to derive a formula for the mean volume of a random simplex in any dimension, providing a new integral representation applicable in higher-dimensional geometry.
Contribution
The paper introduces a generalized integral formula for the mean volume of random simplices in arbitrary dimensions, expanding Efron's original two-dimensional result.
Findings
Derived a cutting plane integral formula for mean volume in higher dimensions
Extended Efron's result from 2D to arbitrary dimensions
Provides a new tool for analyzing random simplices in geometric probability
Abstract
In this short paper, an older Efron's result is extended to obtain a cutting plane integral formula for the mean volume of a random simplex in any d dimensions.
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Taxonomy
TopicsPoint processes and geometric inequalities · Mathematics and Applications · Computational Geometry and Mesh Generation