论文标题
随机双曲线图上的接触过程：亚算力和关键指数
The contact process on random hyperbolic graphs: metastability and critical exponents
论文作者
论文摘要
我们考虑双曲线随机图模型上的接触过程，在学位分布遵守具有指数$χ\ in（1,2）$的功率定律时（以使程度分布具有有限的平均值和无限的第二瞬间）。我们表明，随着感染率的率，非膨胀的概率是零衰减，其指数仅取决于$χ$，并且与配置模型相同，这表明该关键指数的某些普遍性。我们还考虑了双曲线图的有限版本，并证明了亚稳定性结果，因为图形的大小输入了无穷大。
We consider the contact process on the model of hyperbolic random graph, in the regime when the degree distribution obeys a power law with exponent $χ\in(1,2)$ (so that the degree distribution has finite mean and infinite second moment). We show that the probability of non-extinction as the rate of infection goes to zero decays as a power law with an exponent that only depends on $χ$ and which is the same as in the configuration model, suggesting some universality of this critical exponent. We also consider finite versions of the hyperbolic graph and prove metastability results, as the size of the graph goes to infinity.
