Random Assignment Problems on 2d Manifolds

@article{Benedetto2020RandomAP,
  title={Random Assignment Problems on 2d Manifolds},
  author={Dario Benedetto and Emanuele Caglioti and Sergio Caracciolo and Matteo D’Achille and Gabriele Sicuro and Andrea Sportiello},
  journal={arXiv: Mathematical Physics},
  year={2020}
}
We consider the assignment problem between two sets of $N$ random points on a smooth, two-dimensional manifold $\Omega$ of unit area. It is known that the average cost scales as $E_{\Omega}(N)\sim \frac{1}{2\pi}\ln N$ with a correction that is at most of order $\sqrt{\ln N\ln\ln N}$. In this paper, we show that, within the linearization approximation of the field-theoretical formulation of the problem, the first $\Omega$-dependent correction is on the constant term, and can be exactly computed… 
1 Citations
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