具有即时和时滞生灭事件的扩散模型的时空相关性
Space and time correlations for diffusion models with prompt and delayed birth-and-death events
摘要：
了解随机位移和出生和死亡事件的个体集合的统计特性是物理学和生命科学中几个应用的关键，包括核反应堆的诊断和流行病模式的分析。以前的调查的临界政权，出生和死亡的平均平衡，已经表明，高度非泊松波动可能会发生在人口，导致自发的空间聚集，并最终到一个关键的灾难，波动可能会导致灭绝的人口。一个温和的行为时，观察到的人口规模保持不变：波动渐近平稳，避免了关键的灾难。在本文中，我们将扩展这些结果，考虑更广泛的一类模型与及时和延迟的出生和死亡事件，模仿核反应堆物理或孵化inepidemic的前体的存在。我们将考虑有和没有人口控制机制的模型。将推导出密度、两点关联函数和均方对距离的分析或半分析结果，并将其与蒙特卡罗模拟进行比较，后者将用作参考。
英文摘要：
Understanding the statistical properties of a collection of individuals subject to random displacements and birth-and-death events is key to several applications in physics and life sciences, encompassing the diagnostic of nuclear reactors and the analysis of epidemic patterns. Previous investigations of the critical regime, where births and deaths balance on average, have shown that highly non-Poissonian fluctuations might occur in the population, leading to spontaneous spatial clustering, and eventually to a critical catastrophe, where fluctuations can result in the extinction of the population. A milder behaviour is observed when the population size is kept constant: thefluctuations asymptotically level off and the critical catastrophe is averted. In this paper, we shall extend these results by considering the broader class of models with prompt and delayed birth-and-death events, which mimic the presence of precursors in nuclear reactor physics or incubation inepidemics. We shall consider models with and without population control mechanisms. Analytical or semi-analytical results for the density, the two-point correlation function and the mean-squared pair distance will be derived and compared to Monte Carlo simulations, which will be used as a reference.
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