Skip to content
DraconiticResearch
Search Sources API
190,851 studies31 sourcesUpdated 13 min ago
PreprintarXiv licencearXiv

Obstruction to quasi-invariance of Gaussian measures under transport flows on Riemannian Manifolds

  • Anne-Sophie de Suzzoni
  • Mickaël Latocca
Open at sourcePDFDOICite

Abstract

We prove an obstruction to quasi-invariance of Gaussian fields under divergence free transport flows on Riemannian manifolds. For the centered Gaussian field with covariance (1−Δg)−α, α>d/2, quasi-invariance under the transport flow is equivalent to invariance. This happens precisely when the flow acts by isometries, or equivalently when the underlying vector field is Killing. The proof leverages the Feldman--Hájek theorem and utilizes localized pseudo-differential computations. On ℝd this leaves only rigid motions, while on flat tori this leaves only translations.

Related

  1. Multi-marginal optimal transport on sub-Riemannian manifolds
    Haowei Lin
    arXivPreprintarXiv licenceFull textGeometry & topologyOptimisation & controlarXiv
  2. Stability of optimal transport on sub-Riemannian manifolds
    Bang-Xian Han, Zhuo-Nan Zhu
    arXivPreprintarXiv licenceFull textAnalysis & PDEsGeometry & topologyarXiv
  3. Spline interpolation on compact riemannian manifolds
    Charlie Sire, Mike Pereira, Thomas Romary
    Numerical AlgorithmsPeer-reviewedLicence not statedStatisticsHAL
  4. Kernel Density Regression Estimation with Covariates on Riemannian Manifolds
    Gharbi Rihab, Salah Khardani, Mohamed Abdillahi Isman +1
    HALPreprintCC BY 4.0Full textStatisticsHAL
  5. Smoothness estimation for Whittle–Matérn processes on closed Riemannian manifolds
    Moritz Korte-Stapff, Toni Karvonen, Éric Moulines
    Stochastic Processes and their ApplicationsPeer-reviewedLicence not stated3 citedStatisticsHAL

Cite

BibTeXRIS
BibTeX
@misc{suzzoni2026obstruction,
  title = {{Obstruction to quasi-invariance of Gaussian measures under transport flows on Riemannian Manifolds}},
  author = {Anne-Sophie de Suzzoni and Mickaël Latocca},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.01105},
  eprint = {2609.01105},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.01105},
}
RIS
TY  - UNPB
TI  - Obstruction to quasi-invariance of Gaussian measures under transport flows on Riemannian Manifolds
AU  - Anne-Sophie de Suzzoni
AU  - Mickaël Latocca
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.01105
UR  - https://arxiv.org/abs/2609.01105
AB  - We prove an obstruction to quasi-invariance of Gaussian fields under divergence free transport flows on Riemannian manifolds. For the centered Gaussian field with covariance (1−Δ_g)^−α, α>d/2, quasi-invariance under the transport flow is equivalent to invariance. This happens precisely when the flow acts by isometries, or equivalently when the underlying vector field is Killing. The proof leverages the Feldman--Hájek theorem and utilizes localized pseudo-differential computations. On ℝ^d this leaves only rigid motions, while on flat tori this leaves only translations.
ER  -