论文标题
Erdős-rényi图，流行模型与抛物线抛物线漂移之间的新关系
A new relationship between Erdős-Rényi graphs, epidemic models and Brownian motion with parabolic drift
论文作者
论文摘要
在REED-FROST模型（SIR流行病模型的一个例子）中，可以检查一个统计数据，该统计数据计算同时感染个体的数量。该统计量可以根据\ er随机图$ g（n，p）$进行重新重新构成统计量。在Aldous和Martin-Löf的临界窗口中，即当$ p = p = p（n）= n^{ - 1}+λn^{ - 4/3} $时，此统计量的累积总和微弱地收敛到抛物线层流的布朗尼运动的积分。当$ p =（1+λ\ varepsilon_n）/n $每当$ \ varepsilon_n \ to 0 $和$ n^{1/3} \ varepsilon_n_n \ to \ infty $时，相同的统计量将表现出确定性缩放限制。
In the Reed-Frost model, an example of an SIR epidemic model, one can examine a statistic that counts the number of concurrently infected individuals. This statistic can be reformulated as a statistic on the \ER random graph $G(n,p)$. Within the critical window of Aldous and Martin-Löf, i.e. when $p = p(n) = n^{-1}+λn^{-4/3}$, the cumulative sum of this statistic converges weakly to the integral of a Brownian motion with parabolic drift. This same statistic exhibits a deterministic scaling limit when $p = (1+λ\varepsilon_n)/n$ whenever $\varepsilon_n\to 0$ and $n^{1/3}\varepsilon_n\to\infty$.
