New Framework for Interfacial Statistics: Exact n -Point Correlations of Gaussian Level Sets
Abstract
We derive exact analytical expressions for higher-order correlations of Gaussian level-set interfaces, establishing a direct link between bulk field statistics and interface geometry. This framework enables efficient reconstruction of disordered media, detailed modeling of Gaussian foams-structured, double-thresholded interfaces with tunable morphology-and analysis of memory-enhanced anisotropy reflecting directional persistence in the surface structure. These results open new possibilities for characterizing complex transport, guiding stochastic reconstructions, designing materials with desired properties, quantifying the information content of correlation functions, and modeling directional processes on irregular boundaries.
Fields of Study & Subjects
Theoretical and Computational Physics
Statistical Mechanics and Entropy
Point processes and geometric inequalities
Publication details
- Journal / source
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Volume
- 136
- Issue
- 19
- Pages
- 196101–196101
- Publication date
- 3 April 2026
- Language
- EN