Random Riemannian Geometry

Description

We will study random perturbations of Riemannian manifolds (M,g) by means of the so-called “Fractional Gaussian Fields” defined intrinsically by the given manifold. The fields will act on the manifolds via conformal transformation. Our focus will be on the regular case with Hurst parameter H>0, the celebrated Liouville geometry in even dimensions being borderline. We want to understand how basic geometric and functional analytic quantities like diameter, volume, spectral bound, spectral gap, hitting probabilities of the Brownian motions, or heat kernel estimates will change under the influence of the noise. Another goal is to define and analyze in detail the Fractional Gaussian Field on a general Riemannian manifold, a fascinating object of independent interest.

Preprints/Publications

Lorenzo Dello Schiavo, Ronan Herry, Eva Kopfer, Karl-Theodor Sturm: Conformally invariant random fields, quantum Liouville measures, and random Paneitz operators on Riemannian manifolds of even dimension (05/2021)

Lorenzo Dello Schiavo, Eva Kopfer, Karl-Theodor Sturm: A Discovery Tour in Random Riemannian Geometry (12/2020)

Members

  • member's portrait

    Dr. Eva Kopfer

    Rheinische Friedrich-Wilhelms-Universität Bonn
    Principal Investigator
  • member's portrait

    Prof. Dr. Karl-Theodor Sturm

    Rheinische Friedrich-Wilhelms-Universität Bonn
    Principal Investigator
  • member's portrait

    M. Sc. Lorenzo Dello Schiavo

    Institute of Science and Technology Austria
    Associated Scientist
  • member's portrait

    Dr. Ronan Herry

    Rheinische Friedrich-Wilhelms-Universität Bonn
    Associated Scientist

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