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  • Letter
  • Open Access

Level-set percolation of Gaussian random fields on complex networks

Reimer Kühn

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Phys. Rev. E 110, L032301 – Published 3 September, 2024

DOI: https://doi.org/10.1103/PhysRevE.110.L032301

Abstract

We provide an explicit solution of the problem of level-set percolation for multivariate Gaussians defined in terms of weighted graph Laplacians on complex networks. The solution requires an analysis of the heterogeneous microstructure of the percolation problem, i.e., a self-consistent determination of locally varying percolation probabilities. This is achieved using a cavity or message passing approach. It can be evaluated, both for single large instances of locally treelike graphs, and in the thermodynamic limit of random graphs of finite mean degree in the configuration model class.

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Phys. Rev. E 110, L032301– Published 3 September, 2024
  • Received 6 April 2024
  • Revised 6 June 2024
  • Accepted 16 August 2024
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