@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{13145,
  abstract     = {We prove a characterization of the Dirichlet–Ferguson measure over an arbitrary finite diffuse measure space. We provide an interpretation of this characterization in analogy with the Mecke identity for Poisson point processes.},
  author       = {Dello Schiavo, Lorenzo and Lytvynov, Eugene},
  issn         = {1083-589X},
  journal      = {Electronic Communications in Probability},
  pages        = {1--12},
  publisher    = {Institute of Mathematical Statistics},
  title        = {{A Mecke-type characterization of the Dirichlet–Ferguson measure}},
  doi          = {10.1214/23-ECP528},
  volume       = {28},
  year         = {2023},
}

@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},
}

@article{12104,
  abstract     = {We study ergodic decompositions of Dirichlet spaces under intertwining via unitary order isomorphisms. We show that the ergodic decomposition of a quasi-regular Dirichlet space is unique up to a unique isomorphism of the indexing space. Furthermore, every unitary order isomorphism intertwining two quasi-regular Dirichlet spaces is decomposable over their ergodic decompositions up to conjugation via an isomorphism of the corresponding indexing spaces.},
  author       = {Dello Schiavo, Lorenzo and Wirth, Melchior},
  issn         = {1424-3202},
  journal      = {Journal of Evolution Equations},
  number       = {1},
  publisher    = {Springer Nature},
  title        = {{Ergodic decompositions of Dirichlet forms under order isomorphisms}},
  doi          = {10.1007/s00028-022-00859-7},
  volume       = {23},
  year         = {2023},
}

@article{11354,
  abstract     = {We construct a recurrent diffusion process with values in the space of probability measures over an arbitrary closed Riemannian manifold of dimension d≥2. The process is associated with the Dirichlet form defined by integration of the Wasserstein gradient w.r.t. the Dirichlet–Ferguson measure, and is the counterpart on multidimensional base spaces to the modified massive Arratia flow over the unit interval described in V. Konarovskyi and M.-K. von Renesse (Comm. Pure Appl. Math. 72 (2019) 764–800). Together with two different constructions of the process, we discuss its ergodicity, invariant sets, finite-dimensional approximations, and Varadhan short-time asymptotics.},
  author       = {Dello Schiavo, Lorenzo},
  issn         = {2168-894X},
  journal      = {Annals of Probability},
  number       = {2},
  pages        = {591--648},
  publisher    = {Institute of Mathematical Statistics},
  title        = {{The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold}},
  doi          = {10.1214/21-AOP1541},
  volume       = {50},
  year         = {2022},
}

@article{10588,
  abstract     = {We prove the Sobolev-to-Lipschitz property for metric measure spaces satisfying the quasi curvature-dimension condition recently introduced in Milman (Commun Pure Appl Math, to appear). We provide several applications to properties of the corresponding heat semigroup. In particular, under the additional assumption of infinitesimal Hilbertianity, we show the Varadhan short-time asymptotics for the heat semigroup with respect to the distance, and prove the irreducibility of the heat semigroup. These results apply in particular to large classes of (ideal) sub-Riemannian manifolds.},
  author       = {Dello Schiavo, Lorenzo and Suzuki, Kohei},
  issn         = {1432-1807},
  journal      = {Mathematische Annalen},
  keywords     = {quasi curvature-dimension condition, sub-riemannian geometry, Sobolev-to-Lipschitz property, Varadhan short-time asymptotics},
  pages        = {1815--1832},
  publisher    = {Springer Nature},
  title        = {{Sobolev-to-Lipschitz property on QCD- spaces and applications}},
  doi          = {10.1007/s00208-021-02331-2},
  volume       = {384},
  year         = {2022},
}

@article{12177,
  abstract     = {Using elementary hyperbolic geometry, we give an explicit formula for the contraction constant of the skinning map over moduli spaces of relatively acylindrical hyperbolic manifolds.},
  author       = {Cremaschi, Tommaso and Dello Schiavo, Lorenzo},
  issn         = {2330-1511},
  journal      = {Proceedings of the American Mathematical Society, Series B},
  number       = {43},
  pages        = {445--459},
  publisher    = {American Mathematical Society},
  title        = {{Effective contraction of Skinning maps}},
  doi          = {10.1090/bproc/134},
  volume       = {9},
  year         = {2022},
}

@article{10070,
  abstract     = {We extensively discuss the Rademacher and Sobolev-to-Lipschitz properties for generalized intrinsic distances on strongly local Dirichlet spaces possibly without square field operator. We present many non-smooth and infinite-dimensional examples. As an application, we prove the integral Varadhan short-time asymptotic with respect to a given distance function for a large class of strongly local Dirichlet forms.},
  author       = {Dello Schiavo, Lorenzo and Suzuki, Kohei},
  issn         = {1096-0783},
  journal      = {Journal of Functional Analysis},
  number       = {11},
  publisher    = {Elsevier},
  title        = {{Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces}},
  doi          = {10.1016/j.jfa.2021.109234},
  volume       = {281},
  year         = {2021},
}