新的指数控制消光跃迁的准确定性极限
Novel exponents control the quasi-deterministic limit of the extinction transition
摘要：
在标准流行病学模型的框架内，被认为是类灭绝过渡的准确定性限制。随着传染性的增加，易感-感染-易感（SIS）模型表现出从灭绝到传播的转变，由有向渗流等价类描述。我们发现，从过渡点的距离，和控制（垂直）相关长度的发散的前因子，都规模与当地人口的大小，$N$，有两个新的通用指数。SIR模型属于动态渗流类，不同的指数刻画了SIR模型的大$N$行为。广泛的数值研究在一系列的系统导致的猜想，这些特性是通用的，可以用来分类的高密度极限的任何随机过程的边缘灭绝。
英文摘要：
The quasi-deterministic limit of the generic extinction transition is considered within the framework of standard epidemiological models. The susceptible-infected-susceptible (SIS) model is known to exhibit a transition from extinction to spreading, as the infectivity is increased, described by the directed percolation equivalence class. We find that the distance from the transition point, and the prefactor controlling the divergence of the (perpendicular) correlation length, both scale with the local population size, $N$, with two novel universal exponents. Different exponents characterize the large $N$ behavior of the susceptible-infected-recovered (SIR) model, which belongs to the dynamic percolation class. Extensive numerical studies in a range of systems lead to the conjecture that these characteristics are generic and may be used in order to classify the high density limit of any stochastic process on the edge of extinction.
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