Project A01
Energy solutions, singular SPDEs on large scales and stochastic homogenization

Project description

While we now have a good understanding of pathwise local properties of scaling subcritical singular SPDEs, probabilistic aspects and long-term/large-scale behavior remain less clear. Energy solutions offer a probabilistic view for some singular SPDEs, based on martingale arguments and Fock space analysis. Our project will further develop the theory of energy solutions and focus on homogenisation of non-symmetric SDEs. A key objective is to explore dissipative effects of Burgers nonlinearities in Fock space and to analyze the well-posedness and non-Gaussianity of critical and supercritical singular SPDEs.

Principal Investigators

Felix Otto (MPI Leipzig)

Nicolas Perkowski (FU Berlin)

Project members

Rhys Steele (MPI Leipzig)

Immanuel Zachhuber (FU Berlin)

Guilherme de Lima Feltes (FU Berlin) - associated member

Publications

Preprints

• Zachhuber, I., 2025. On domains of elliptic operators with distributional coefficients. https://doi.org/10.48550/ARXIV.2509.24950 

• De Vecchi, F. C., Ji, X., Zachhuber, I., 2025. Stochastic Hartree NLS in 3d coming from a Many-Body Quantum System with White Noise Potential. https://doi.org/10.48550/ARXIV.2505.01157 

• Gräfner, L., Perkowski, N., Popat, S., 2024. Energy solutions of singular SPDEs on Hilbert spaces with applications to domains with boundary conditions. https://doi.org/10.48550/ARXIV.2411.07680

• Gräfner, L., Perkowski, N., 2024. Weak well-posedness of energy solutions to singular SDEs with supercritical distributional drift. https://doi.org/10.48550/ARXIV.2407.09046