{
  "id": "1805.02593",
  "version": "v1",
  "published": "2018-05-07T16:07:45.000Z",
  "updated": "2018-05-07T16:07:45.000Z",
  "title": "Reflection negative kernels and fractional Brownian motion",
  "authors": [
    "P. Jorgensen",
    "K. -H. Neeb",
    "G. Olafsson"
  ],
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "In this article we study the connection of fractional Brownian motion, representation theory and reflection positivity in quantum physics. We introduce and study reflection positivity for affine isometric actions of a Lie group on a Hilbert space E and show in particular that fractional Brownian motion for Hurst index 0<H\\le 1/2 is reflection positive and leads via reflection positivity to an infinite dimensional Hilbert space if 0<H <1/2. We also study projective invariance of fractional Brownian motion and relate this to the complementary series representations of GL(2,R). We relate this to a measure preserving action on a Gaussian L^2-Hilbert space L^2(E).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-07T16:07:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A35",
      "43A65",
      "60G15",
      "81T08"
    ],
    "keywords": [
      "fractional brownian motion",
      "reflection negative kernels",
      "infinite dimensional hilbert space",
      "complementary series representations",
      "study reflection positivity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}