@article{14934,
  abstract     = {We study random perturbations of a Riemannian manifold (M, g) by means of so-called
Fractional Gaussian Fields, which are defined intrinsically by the given manifold. The fields
h• : ω → hω will act on the manifold via the conformal transformation g → gω := e2hω g.
Our focus will be on the regular case with Hurst parameter H > 0, the critical case H = 0
being the celebrated Liouville geometry in two dimensions. We want to understand how basic
geometric and functional-analytic quantities like diameter, volume, heat kernel, Brownian
motion, spectral bound, or spectral gap change under the influence of the noise. And if so, is
it possible to quantify these dependencies in terms of key parameters of the noise? Another
goal is to define and analyze in detail the Fractional Gaussian Fields on a general Riemannian
manifold, a fascinating object of independent interest.},
  author       = {Dello Schiavo, Lorenzo and Kopfer, Eva and Sturm, Karl Theodor},
  issn         = {1572-929X},
  journal      = {Potential Analysis},
  publisher    = {Springer Nature},
  title        = {{A discovery tour in random Riemannian geometry}},
  doi          = {10.1007/s11118-023-10118-0},
  year         = {2024},
}

@article{10145,
  abstract     = {We study direct integrals of quadratic and Dirichlet forms. We show that each quasi-regular Dirichlet space over a probability space admits a unique representation as a direct integral of irreducible Dirichlet spaces, quasi-regular for the same underlying topology. The same holds for each quasi-regular strongly local Dirichlet space over a metrizable Luzin σ-finite Radon measure space, and admitting carré du champ operator. In this case, the representation is only projectively unique.},
  author       = {Dello Schiavo, Lorenzo},
  issn         = {1572-929X},
  journal      = {Potential Analysis},
  pages        = {573--615},
  publisher    = {Springer Nature},
  title        = {{Ergodic decomposition of Dirichlet forms via direct integrals and applications}},
  doi          = {10.1007/s11118-021-09951-y},
  volume       = {58},
  year         = {2023},
}