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PreprintarXiv licencearXiv

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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Cite

BibTeXRIS
BibTeX
@misc{cheng2026geometrically,
  title = {{A geometrically linear approximation of min-max optimal matching}},
  author = {Xiaopeng Cheng and Felix Otto and Matteo Palmieri and Arthur Wachtel},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08680},
  eprint = {2609.08680},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08680},
}
RIS
TY  - UNPB
TI  - A geometrically linear approximation of min-max optimal matching
AU  - Xiaopeng Cheng
AU  - Felix Otto
AU  - Matteo Palmieri
AU  - Arthur Wachtel
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.08680
UR  - https://arxiv.org/abs/2609.08680
AB  - 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.
ER  -