论文标题
持续Lotka中随机矩阵普遍性的崩溃 - 沃尔特拉社区
Breakdown of random-matrix universality in persistent Lotka--Volterra communities
论文作者
论文摘要
随机矩阵的特征值频谱通常仅取决于其元素的第一矩和第二矩，而不取决于它们绘制的特定分布。这种普遍性原则的有效性通常是在没有证明的情况下假定的。在这封信中，我们在广义的Lotka-volterra方程中提供了相关的反例。使用动态平均场理论，我们得出了进化的生态群落中物种之间相互作用的统计数据。然后，我们表明，除了高斯集合之外，这些相互作用的完整统计数据需要正确预测特征值频谱并因此稳定性。因此，通用原则在该系统中失败。因此，我们表明，随机矩阵的特征值光谱可用于推断“可行”生态群落的稳定性，但前提是考虑到出现的对物种之间相互作用的非高斯统计。
The eigenvalue spectrum of a random matrix often only depends on the first and second moments of its elements, but not on the specific distribution from which they are drawn. The validity of this universality principle is often assumed without proof in applications. In this letter, we offer a pertinent counterexample in the context of the generalised Lotka--Volterra equations. Using dynamic mean-field theory, we derive the statistics of the interactions between species in an evolved ecological community. We then show that the full statistics of these interactions, beyond those of a Gaussian ensemble, are required to correctly predict the eigenvalue spectrum and therefore stability. Consequently, the universality principle fails in this system. We thus show that the eigenvalue spectra of random matrices can be used to deduce the stability of `feasible' ecological communities, but only if the emergent non-Gaussian statistics of the interactions between species are taken into account.
