AI 中文总结
本文通过几何线性近似和对偶公式，建立了临界维度下极小极大最优匹配与随机曲线作用的关系，提取了期望成本的首阶渐近项，改进了先前结果。
AI 中文摘要
本文建立了临界维度$d=2$下极小极大最优匹配与布朗势中随机曲线的更简单、几何线性作用之间的联系。我们遵循Leighton和Shor的方法，采用对偶公式，并将其近似为一个具有白噪声特征的随机体积项的等周型问题。这使我们能够提取期望成本渐近中的首阶项，从而改进了先前的结果。
英文摘要
In this work we establish a connection between the min-max optimal matching in the critical dimension $d=2$ and a simpler, geometrically linear, action of random curves in a Brownian potential. This is done by following Leighton and Shor and working with the dual formulation, which we approximate by a problem of isoperimetric-type with a random volume term of white-noise character. This allows us to extract the leading-order term in the asymptotics of the expected cost, sharpening previous results.
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