分类： 数学 >> 统计和概率 提交时间： 2021-12-16
摘要： The paper considers Wasserstein metric between the empirical probability measure of n discrete random variables and a continuous uniform one on the d-dimensional ball and give the asymptotic estimation of their expectation as $n \to \infty$. Further We considers the above problem on a mixed process, i.e., n discrete random variables are produced by the Poisson process.
分类： 数学 >> 应用数学 提交时间： 2021-12-15
摘要： We analyze properties of degree and clustering of a hyperbolic geometric model of complex networks in small parameter case $\tau<1, 2\sigma<1$. We find that the probability of k-degree goes to 0 and the global clustering coefficient goes to 0 in probability too as the number of nodes $N\to\infty$ for some specific growth $R(N)$ of the region radius. Here the scale-free degree is failed and the connection between neighbors are very weak. The transition of properties of the model with the parameter $\sigma$ changes seems to show that the mobility is important to keep society full and stable communication, otherwise a silence society. Some analysis technique and method are first applied for such model.
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