Random Geometric Graphs in Reflexive Banach Spaces

arXiv - MATH - Functional Analysis Pub Date : 2024-09-06 DOI:arxiv-2409.04237

József Balogh, Mark Walters, András Zsák

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Abstract

We investigate a random geometric graph model introduced by Bonato and Janssen. The vertices are the points of a countable dense set $S$ in a (necessarily separable) normed vector space $X$, and each pair of points are joined independently with some fixed probability $p$ (with $0

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反身巴拿赫空间中的随机几何图形

我们研究了博纳托和扬森提出的随机几何图模型。顶点是一个（必然是可分离的）规范向量空间 $X$中的可数稠密集 $S$ 的点，如果每一对点之间的距离小于 $1$，则以某种固定概率 $p$ 独立连接（$0

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