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<p>We study a generalization of the multi-marginal optimal transport problem, which has no fixed number of marginals <i>N</i> and is inspired of statistical mechanics. It consists in optimizing a linear combination of the costs for all the possible <i>N</i>’s, while fixing a certain linear combination of the corresponding marginals.</p>

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Grand-Canonical Optimal Transport

  • 期刊论文

  • 发表日期：

    2025年1月13日

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  • Simone Di Marino,
  • Mathieu Lewin,
  • Luca Nenna

摘要

We study a generalization of the multi-marginal optimal transport problem, which has no fixed number of marginals N and is inspired of statistical mechanics. It consists in optimizing a linear combination of the costs for all the possible N’s, while fixing a certain linear combination of the corresponding marginals.