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PreprintarXiv licencearXiv

A New Framework for Interfacial Statistics: Exact n-Point Correlations of Gaussian Level Sets

  • Aleksei M. Cherkasov
  • Kirill M. Gerke
  • Aleksey Khlyupin
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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.

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Cite

BibTeXRIS
BibTeX
@misc{cherkasov2026framework,
  title = {{A New Framework for Interfacial Statistics: Exact n-Point Correlations of Gaussian Level Sets}},
  author = {Aleksei M. Cherkasov and Kirill M. Gerke and Aleksey Khlyupin},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14586},
  eprint = {2609.14586},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14586},
}
RIS
TY  - UNPB
TI  - A New Framework for Interfacial Statistics: Exact n-Point Correlations of Gaussian Level Sets
AU  - Aleksei M. Cherkasov
AU  - Kirill M. Gerke
AU  - Aleksey Khlyupin
PY  - 2026
DA  - 2026/09/13
PB  - arXiv
DO  - 10.48550/arxiv.2609.14586
UR  - https://arxiv.org/abs/2609.14586
AB  - 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.
ER  -