The study of real-life network modeling has become very popular in recent years. An attractive model is the scale-free percolation model on the lattice \({\mathbb Z}^d\), \(d\ge 1\), because it fulfills several stylized facts observed in large real-life networks. We adopt this model to continuum space which leads to a heterogeneous random-connection model on \({\mathbb R}^d\): Particles are generated by a homogeneous marked Poisson point process on \({\mathbb R}^d\), and the probability of an edge between two particles is determined by their marks and their distance. In this model we study several properties such as the degree distributions, percolation properties and graph distances.

中文翻译：

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连续空间中的无标度渗流

近年来，对现实生活中的网络建模的研究变得非常流行。一个有吸引力的模型是晶格\（{\ mathbb Z} ^ d \），\（d \ ge 1 \）上的无标度渗流模型，因为它可以满足在大型现实网络中观察到的几种风格化事实。我们将此模型用于连续空间，从而导致\（{\ mathbb R} ^ d \）上的异构随机连接模型：粒子是通过\（{\ mathbb R} ^ d \上的同质标记泊松点过程生成的），两个粒子之间的边缘概率由其标记和距离确定。在此模型中，我们研究了多个属性，例如度分布，渗滤属性和图形距离。