Lazy random walks and optimal transport on graphs

• Léonard, Christian ^[1]
  1. [1] Paris West University Nanterre La Défense

     Paris West University Nanterre La Défense

     París, Francia

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 44, Nº. 3, 2016, págs. 1864-1915
• Idioma: inglés
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• Resumen

  • This paper is about the construction of displacement interpolations of probability distributions on a discrete metric graph. Our approach is based on the approximation of any optimal transport problem whose cost function is a distance on a discrete graph by a sequence of entropy minimization problems under marginal constraints, called Schrödinger problems, which are associated with random walks. Displacement interpolations are defined as the limit of the time-marginal flows of the solutions to the Schrödinger problems as the jump frequencies of the random walks tend down to zero. The main convergence results are based on Γ-convergence of entropy minimization problems.

    As a by-product, we obtain new results about optimal transport on graphs.