It is known that for Kn,n equipped with i.i.d. exp (1) edge costs, the minimum total cost of a perfect matching converges to $\zeta(2)=\pi^2/6$ in probability. Similar convergence has been established for all edge cost distributions of pseudo-dimension $q \geq 1$ . In this paper we extend those results to all real positive q, confirming the Mézard–Parisi conjecture in the last remaining applicable case.

中文翻译：

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伪维度 0 < q < 1 的最小完美匹配

据了解，对于ķn,n配备 iid exp (1) 边成本，完美匹配的最小总成本收敛于$\zeta(2)=\pi^2/6$在概率上。已经为所有边缘成本分布建立了类似的收敛伪维度$q \geq 1$. 在本文中，我们将这些结果扩展到所有真正的积极q，证实了最后一个适用案例中的 Mézard-Parisi 猜想。