{
  "id": "1705.04825",
  "version": "v1",
  "published": "2017-05-13T13:41:16.000Z",
  "updated": "2017-05-13T13:41:16.000Z",
  "title": "Geometric mean flows and the Cartan barycenter on the Wasserstein space over positive definite matrices",
  "authors": [
    "Fumio Hiai",
    "Yongdo Lim"
  ],
  "comment": "14 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We introduce a class of flows on the Wasserstein space of probability measures with finite first moment on the Cartan-Hadamard Riemannian manifold of positive definite matrices, and consider the problem of differentiability of the corresponding Cartan barycentric trajectory. As a consequence we have a version of Lie-Trotter formula and a related unitarily invariant norm inequality. Furthermore, a fixed point theorem related to the Karcher equation and the Cartan barycentric trajectory is also presented as an application.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-13T13:41:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A42",
      "47A64",
      "47B65",
      "47L07"
    ],
    "keywords": [
      "positive definite matrices",
      "geometric mean flows",
      "wasserstein space",
      "cartan barycenter",
      "unitarily invariant norm inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}