{
  "id": "2105.11377",
  "version": "v1",
  "published": "2021-05-24T16:10:42.000Z",
  "updated": "2021-05-24T16:10:42.000Z",
  "title": "Local mixing of one-parameter diagonal flows on Anosov homogeneous spaces",
  "authors": [
    "Michael Chow",
    "Pratyush Sarkar"
  ],
  "comment": "44 pages, 1 figure",
  "categories": [
    "math.DS",
    "math.GT",
    "math.SP"
  ],
  "abstract": "Let $G$ be a connected semisimple real algebraic group and $\\Gamma < G$ be an Anosov subgroup with respect to a minimal parabolic subgroup. We prove local mixing of the one-parameter diagonal flow $\\{\\exp(t\\mathsf{v}) : t \\in \\mathbb{R}\\}$ on $\\Gamma \\backslash G$ in any interior direction $\\mathsf{v}$ of the limit cone of $\\Gamma$ with respect to the Bowen--Margulis--Sullivan measure associated to $\\mathsf{v}$. When $\\Gamma$ is the fundamental group of a compact negatively curved manifold, this was proved earlier by Sambarino for $M$-invariant functions, where $M$ is the centralizer of the flow. By the work of Edwards--Lee--Oh which is a higher rank extension of Roblin's transverse intersection argument, an immediate application is an asymptotic formula for matrix coefficients in $L^2(\\Gamma \\backslash G)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-24T16:10:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A17",
      "37A25",
      "37C30",
      "37D20"
    ],
    "keywords": [
      "one-parameter diagonal flow",
      "anosov homogeneous spaces",
      "local mixing",
      "connected semisimple real algebraic group",
      "roblins transverse intersection argument"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}