A geometrically linear approximation of min-max optimal matching

Xiaopeng Cheng; Felix Otto; Matteo Palmieri; Arthur Wachtel

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arXiv · 2609.08680

A geometrically linear approximation of min-max optimal matching

Xiaopeng Cheng·Felix Otto·Matteo Palmieri·Arthur Wachtel

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Abstract

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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Xiaopeng Cheng, Felix Otto, Matteo Palmieri, Arthur Wachtel. 2026-09-08. A geometrically linear approximation of min-max optimal matching. https://arxiv.org/abs/2609.08680

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