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引用次数: 0
摘要
我们解决了在平面上定义的高斯分布的指数为 2 的随机欧氏匹配问题。勒杜(Ledoux)和塔拉格朗(Talagrand)之前的研究确定了平均成本的领先行为,直到一个乘法常数。我们明确地确定了这个常数,表明平均成本与 \((\log \, N)^2,\) 成正比,其中 N 是点的数量。我们的方法依赖于几何分解,允许明确计算常数。我们的结果表明,对于许多定义在平面无界域上的分布,随机匹配问题有可能得到精确的解决。
Random Matching in 2D with Exponent 2 for Gaussian Densities
We solve the Random Euclidean Matching problem with exponent 2 for the Gaussian distribution defined on the plane. Previous works by Ledoux and Talagrand determined the leading behavior of the average cost up to a multiplicative constant. We explicitly determine the constant, showing that the average cost is proportional to \((\log \, N)^2,\) where N is the number of points. Our approach relies on a geometric decomposition allowing an explicit computation of the constant. Our results illustrate the potential for exact solutions of random matching problems for many distributions defined on unbounded domains on the plane.
期刊介绍:
The Journal of Statistical Physics publishes original and invited review papers in all areas of statistical physics as well as in related fields concerned with collective phenomena in physical systems.