A 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 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 modelling directional processes on irregular boundaries.

arXiv commentPublished in Phys. Rev. Lett. 136, 196101 (2026), 7 pages, 4 figures

References in corpus (6)

• A Superior Descriptor of Random Textures and Its Predictive Capacity
• Statistical reconstruction of three-dimensional porous media from two-dimensional images
• Transport properties of heterogeneous materials derived from Gaussian random fields: Bounds and Simulation
• Precise algorithms to compute surface correlation functions of two-phase heterogeneous media and their applications
• Adaptive phase-retrieval stochastic reconstruction with correlation functions: 3D images from 2D cuts
• Random Process Theory Approach to Geometric Heterogeneous Surfaces: Effective Fluid-Solid Interaction