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arXiv · 1403.3635

The Minimum Perfect Matching in Pseudo-dimension $0<q<1$

Joel Larsson
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Abstract

It is known that for $K_{n,n}$ equipped with i.i.d. $exp(1)$ edge costs, the minimum total cost of a perfect matching converges to $π^2/6$ in probability. Similar convergence has been established for all edge cost distributions of pseudo-dimension $q \geq 1$, such as Wei(1,q) costs. In this paper we extend those results all $q>0$, confirming the Mézard-Parisi conjecture in the last remaining applicable case.

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Joel Larsson. 2019-06-12. The Minimum Perfect Matching in Pseudo-dimension $0<q<1$. https://arxiv.org/abs/1403.3635

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