注意广义随机多边形的方差

IF 0.9 3区数学 Q2 MATHEMATICS

Aequationes Mathematicae Pub Date : 2025-01-10 DOI:10.1007/s00010-024-01147-0

Ferenc Fodor, Balázs Grünfelder

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引用次数: 0

摘要

我们考虑一个概率模型，在这个模型中，来自一个凸盘K的样本的i. id个均匀随机点的壳由包含该样本的另一个合适的固定凸盘L的所有平移的交集形成。我们假设K和L都有\(C^2_+\)光滑的边界，并证明了在不同曲率条件下随机L多边形顶点数和缺失面积方差的上界。我们也把我们的一些结果转移到这个模型的一个限定变体上。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Note on the variance of generalized random polygons

We consider a probability model in which the hull of a sample of i.i.d. uniform random points from a convex disc K is formed by the intersection of all translates of another suitable fixed convex disc L that contain the sample. Such an object is called a random L-polygon in K. We assume that both K and L have \(C^2_+\) smooth boundaries, and we prove upper bounds on the variance of the number of vertices and missed area of random L-polygons assuming different curvature conditions. We also transfer some of our result to a circumscribed variant of this model.

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来源期刊

Aequationes Mathematicae MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.70

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： aequationes mathematicae is an international journal of pure and applied mathematics, which emphasizes functional equations, dynamical systems, iteration theory, combinatorics, and geometry. The journal publishes research papers, reports of meetings, and bibliographies. High quality survey articles are an especially welcome feature. In addition, summaries of recent developments and research in the field are published rapidly.