Geometric random intersection graphs with general connection probabilities

IF 0.7 4区 数学 Q3 STATISTICS & PROBABILITY
Maria Deijfen, Riccardo Michielan
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引用次数: 0

Abstract

Let $\mathcal{V}$ and $\mathcal{U}$ be the point sets of two independent homogeneous Poisson processes on $\mathbb{R}^d$ . A graph $\mathcal{G}_\mathcal{V}$ with vertex set $\mathcal{V}$ is constructed by first connecting pairs of points (v, u) with $v\in\mathcal{V}$ and $u\in\mathcal{U}$ independently with probability $g(v-u)$ , where g is a non-increasing radial function, and then connecting two points $v_1,v_2\in\mathcal{V}$ if and only if they have a joint neighbor $u\in\mathcal{U}$ . This gives rise to a random intersection graph on $\mathbb{R}^d$ . Local properties of the graph, including the degree distribution, are investigated and quantified in terms of the intensities of the underlying Poisson processes and the function g. Furthermore, the percolation properties of the graph are characterized and shown to differ depending on whether g has bounded or unbounded support.
具有一般连接概率的几何随机相交图
让 $\mathcal{V}$ 和 $\mathcal{U}$ 是 $\mathbb{R}^d$ 上两个独立同质泊松过程的点集。首先以 $g(v-u)$ 的概率将 $v\in\mathcal{V}$ 和 $u\in\mathcal{U}$ 独立的点对 (v, u) 连接起来,就构建了一个顶点集为 $\mathcal{V}$ 的图 $\mathcal{G}_\mathcal{V}$ 、其中 g 是一个非递增的径向函数,然后连接两个点 $v_1,v_2\in\mathcal{V}$ 当且仅当它们有一个共同的邻居 $u\in\mathcal{U}$ 。这就产生了 $\mathbb{R}^d$ 上的随机交集图。此外,该图的渗流特性根据 g 的有界或无界支持而有所不同。
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来源期刊
Journal of Applied Probability
Journal of Applied Probability 数学-统计学与概率论
CiteScore
1.50
自引率
10.00%
发文量
92
审稿时长
6-12 weeks
期刊介绍: Journal of Applied Probability is the oldest journal devoted to the publication of research in the field of applied probability. It is an international journal published by the Applied Probability Trust, and it serves as a companion publication to the Advances in Applied Probability. Its wide audience includes leading researchers across the entire spectrum of applied probability, including biosciences applications, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, the physical and social sciences, and any field where stochastic modeling is used. A submission to Applied Probability represents a submission that may, at the Editor-in-Chief’s discretion, appear in either the Journal of Applied Probability or the Advances in Applied Probability. Typically, shorter papers appear in the Journal, with longer contributions appearing in the Advances.
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