A Complete Proof of the Limit Formula for Observable Diameter
Shigeaki Yokota
TL;DR
This paper corrects a key inequality in the proof of the limit formula for observable diameters of pyramids, providing a complete and verified proof of the formula under weak convergence.
Contribution
It offers a corrected and complete proof of the limit formula for observable diameters, addressing previous gaps and counterexamples.
Findings
Corrected the inequality used in the original proof.
Verified the limit formula for observable diameters.
Provided a constructive counterexample to previous assumptions.
Abstract
Ozawa and Shioya proposed the limit formula for observable diameters of pyramids under weak convergence. However, we find a constructive counterexample to an inequality used in their proof. In this paper, we correct the inequality and verify the limit formula.
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Taxonomy
TopicsProbabilistic and Robust Engineering Design · Point processes and geometric inequalities · Advanced Optimization Algorithms Research