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The Monge--Kantorovich problem, the Schur--Horn theorem, and the diffeomorphism group of the annulus

Anthony M. Bloch, Tudor S. Ratiu

17/4/25 Published in : arXiv:2504.12924

First, we analyze the discrete Monge--Kantorovich problem, linking it with the minimization problem of linear functionals over adjoint orbits. Second, we consider its generalization to the setting of area preserving diffeomorphisms of the annulus. In both cases, we show how the problem can be linked to permutohedra, majorization, and to gradient flows with respect to a suitable metric.

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Phase I & II research project(s)

  • Quantum Systems
  • Field Theory
  • Geometry, Topology and Physics

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  • Holography and bulk-boundary correspondence

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Noise sensitivity of crossings for high temperature Ising model

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The National Centres of Competence in Research (NCCRs) are a funding scheme of the Swiss National Science Foundation

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