论文标题
部分可观测时空混沌系统的无模型预测
Asymptotics of $k$-nearest neighbor Riesz energies
论文作者
论文摘要
我们获得了有关$ n $粒子系统的新渐近结果，该系统由涉及$ k $ neart nearbor的$ k $ neart邻居的$ n \ neart nearbors的系统，作为$ n \ to \ infty $。这些结果包括对具有外部场的加权Riesz电位的概括。这种互动为降低$ n $体相互作用的计算复杂性的其他方法提供了一种吸引人的替代方法。我们发现了大$ n $渐近器的一阶术语，并表征了最小化器的限制分布。我们还获得了有关此类相互作用的$γ$ convergence的结果，并在没有外部场的情况下描述了一维平坦的圆环上的最小化器。
We obtain new asymptotic results about systems of $ N $ particles governed by Riesz interactions involving $ k $-nearest neighbors of each particle as $N\to\infty$. These results include a generalization to weighted Riesz potentials with external field. Such interactions offer an appealing alternative to other approaches for reducing the computational complexity of an $ N $-body interaction. We find the first-order term of the large $ N $ asymptotics and characterize the limiting distribution of the minimizers. We also obtain results about the $ Γ$-convergence of such interactions, and describe minimizers on the 1-dimensional flat torus in the absence of external field, for all $ N $.
