Project A03
Random interface models, scaling limits and large deviations

Project description

We model a random interface as the graph of a random function Φ: B->Z^d, where B is a large box in Z^d. The aim is to study the asymptotic properties of these models, particularly rescaling the anharmonic Laplace interaction model, constructing the |∇ Φ|^p model, and assessing the impact of a Poisson point process as basis. For both models, large-scale behaviors such as isotropy and stiffness are explored in the context of large deviations. 

Principal Investigators

Jean-Dominique Deuschel (TU Berlin)

Wolfgang König (TU Berlin)

Barbara Zwicknagl (HU Berlin)

Project members

Jonas Lautenschläger (HU Berlin)

Mengzi Xie (TU Berlin)

Anastasija Pesic (WIAS) - associated member

Publications

• Ginster, J., Koser, M., & Zwicknagl, B., 2026. Microstructures in a two-dimensional frustrated spin system: Scaling regimes and a discrete-to-continuum limit. ESAIM: Control, Optimisation and Calculus of Variations, 32, 49. https://doi.org/10.1051/cocv/2026015 

• Deuschel, J.-D., Kumagai, T., & Slowik, M., 2026. Gradient estimates of the heat kernel for random walks among time-dependent random conductances. Probability Theory and Related Fields. https://doi.org/10.1007/s00440-026-01499-5 

Preprints

• Deuschel, J.-D., Thierbach, C., & Zwicknagl, B., 2026. A Variational Characterization of a Gibbs measure related to the Aviles-Giga Functional. https://doi.org/10.48550/ARXIV.2608.01860